# RD Sharma solutions for Class 10 Maths chapter 11 - Trigonometric Identities [Latest edition]

## Solutions for Chapter 11: Trigonometric Identities

Below listed, you can find solutions for Chapter 11 of CBSE RD Sharma for Class 10 Maths.

Exercise 11.1Exercise 11.2Exercise 11.3Exercise 11.4
Exercise 11.1 [Pages 43 - 47]

### RD Sharma solutions for Class 10 Maths Chapter 11 Trigonometric Identities Exercise 11.1 [Pages 43 - 47]

Exercise 11.1 | Q 1 | Page 43

Prove the following trigonometric identities:

(1 - cos^2 A) cosec^2 A = 1

Exercise 11.1 | Q 2 | Page 43

Prove the following trigonometric identities

(1 + cot2 A) sin2 A = 1

Exercise 11.1 | Q 3 | Page 43

Prove the following trigonometric identities.

tan2θ cos2θ = 1 − cos2θ

Exercise 11.1 | Q 4 | Page 43

Prove the following trigonometric identities.

cosec theta sqrt(1 - cos^2 theta) = 1

Exercise 11.1 | Q 5 | Page 43

Prove the following trigonometric identities.

(sec2 θ − 1) (cosec2 θ − 1) = 1

Exercise 11.1 | Q 6 | Page 43

Prove the following trigonometric identities.

tan theta + 1/tan theta = sec theta cosec theta

Exercise 11.1 | Q 7 | Page 43

Prove the following trigonometric identities

cos theta/(1 - sin theta) = (1 + sin theta)/cos theta

Exercise 11.1 | Q 8 | Page 43

Prove the following trigonometric identities.

cos theta/(1 + sin theta) = (1 - sin theta)/cos theta

Exercise 11.1 | Q 9 | Page 43

Prove the following trigonometric identity.

cos^2 A + 1/(1 + cot^2 A) = 1

Exercise 11.1 | Q 10 | Page 43

Prove the following trigonometric identities.

sin^2 A + 1/(1 + tan^2 A) = 1

Exercise 11.1 | Q 11 | Page 43

Prove the following trigonometric identities.

sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta

Exercise 11.1 | Q 12 | Page 43

Prove the following trigonometric identities.

(1 - cos theta)/sin theta = sin theta/(1 + cos theta)

Exercise 11.1 | Q 13 | Page 44

Prove the following trigonometric identities.

sin theta/(1 - cos theta) =  cosec theta + cot theta

Exercise 11.1 | Q 14 | Page 44

Prove the following trigonometric identities.

(1 - sin theta)/(1 + sin theta) = (sec theta - tan theta)^2

Exercise 11.1 | Q 15 | Page 44

Prove the following trigonometric identities.

(cosecθ + sinθ) (cosecθ − sinθ) = cot2 θ + cos2θ

Exercise 11.1 | Q 16 | Page 44

Prove the following trigonometric identities.

((1 + cot^2 theta) tan theta)/sec^2 theta = cot theta

Exercise 11.1 | Q 17 | Page 44

Prove the following trigonometric identities.

(secθ + cosθ) (secθ − cosθ) = tan2θ + sin2θ

Exercise 11.1 | Q 18 | Page 44

Prove the following trigonometric identities.

sec A (1 − sin A) (sec A + tan A) = 1

Exercise 11.1 | Q 19 | Page 44

Prove the following trigonometric identities.

(cosecA − sinA) (secA − cosA) (tanA + cotA) = 1

Exercise 11.1 | Q 20 | Page 44

Prove the following trigonometric identities.

tan^2 theta - sin^2 theta tan^2 theta sin^2 theta

Exercise 11.1 | Q 21 | Page 44

Prove the following trigonometric identities.

(1 + tan2θ) (1 − sinθ) (1 + sinθ) = 1

Exercise 11.1 | Q 22 | Page 44

Prove the following trigonometric identities.

sin2 A cot2 A + cos2 A tan2 A = 1

Exercise 11.1 | Q 23.1 | Page 44

Prove the following trigonometric identities.

cot theta - tan theta = (2 cos^2 theta - 1)/(sin theta cos theta)

Exercise 11.1 | Q 23.2 | Page 44

Prove the following trigonometric identities.

tan theta - cot theta = (2 sin^2 theta - 1)/(sin theta cos theta)

Exercise 11.1 | Q 24 | Page 44

Prove the following trigonometric identities.

(cos^2 theta)/sin theta - cosec theta +  sin theta  = 0

Exercise 11.1 | Q 25 | Page 44

Prove the following trigonometric identities.

1/(1 + sin A) + 1/(1 - sin A) =  2sec^2 A

Exercise 11.1 | Q 26 | Page 44

Prove the following trigonometric identities.

(1 + sin theta)/cos theta + cos theta/(1 + sin theta) = 2 sec theta

Exercise 11.1 | Q 27 | Page 44

Prove the following trigonometric identities

((1 + sin theta)^2 + (1 + sin theta)^2)/(2cos^2 theta) =  (1 + sin^2 theta)/(1 - sin^2 theta)

Exercise 11.1 | Q 28 | Page 44

Prove the following trigonometric identities

(1 + tan^2 theta)/(1 + cot^2 theta) = ((1 - tan theta)/(1 - cot theta))^2 = tan^2 theta

Exercise 11.1 | Q 29 | Page 44

Prove the following trigonometric identities.

(1 + sec theta)/sec theta = (sin^2 theta)/(1 - cos theta)

Exercise 11.1 | Q 30 | Page 44

Prove the following trigonometric identities.

tan theta/(1 - cot theta) + cot theta/(1 - tan theta) = 1 + tan theta + cot theta

Exercise 11.1 | Q 31 | Page 44

Prove the following trigonometric identities.

sec6θ = tan6θ + 3 tan2θ sec2θ + 1

Exercise 11.1 | Q 32 | Page 44

Prove the following trigonometric identities

cosec6θ = cot6θ + 3 cot2θ cosec2θ + 1

Exercise 11.1 | Q 33 | Page 44

Prove the following trigonometric identities.

((1 + tan^2 theta)cot theta)/(cosec^2 theta)   = tan theta

Exercise 11.1 | Q 34 | Page 44

Prove the following trigonometric identities.

(1 + cos A)/sin^2 A = 1/(1 - cos A)

Exercise 11.1 | Q 35 | Page 44

Prove the following trigonometric identities.

(sec A - tan A)/(sec A + tan A) = (cos^2 A)/(1 + sin A)^2

Exercise 11.1 | Q 36 | Page 44

Prove the following trigonometric identities.

(1 + cos A)/sin A = sin A/(1 - cos A)

Exercise 11.1 | Q 37 | Page 44

Prove the following trigonometric identities.

sqrt((1 + sin A)/(1 - sin A)) = sec A + tan A

Exercise 11.1 | Q 38 | Page 44

Prove the following trigonometric identities.

sqrt((1 - cos A)/(1 + cos A)) = cosec A - cot A

Exercise 11.1 | Q 39 | Page 45

Prove the following trigonometric identities.

(sec A - tan A)^2 = (1 - sin A)/(1 +  sin A)

Exercise 11.1 | Q 40 | Page 45

Prove the following trigonometric identities. (1 - cos A)/(1 + cos A) = (cot A - cosec A)^2

Exercise 11.1 | Q 41 | Page 45

Prove the following trigonometric identities.

1/(sec A - 1) + 1/(sec A + 1) = 2 cosec A cot A

Exercise 11.1 | Q 42 | Page 45

Prove the following trigonometric identities.

cos A/(1 - tan A) + sin A/(1 - cot A)  = sin A + cos A

Exercise 11.1 | Q 43 | Page 45

Prove the following trigonometric identities.

(cosec A)/(cosec A  - 1) + (cosec A)/(cosec A = 1) = 2 sec^2 A

Exercise 11.1 | Q 44 | Page 45

Prove the following trigonometric identities.

(1 + tan^2 A) + (1 + 1/tan^2 A) = 1/(sin^2 A - sin^4 A)

Exercise 11.1 | Q 45 | Page 45

Prove the following trigonometric identities.

(tan^2 A)/(1 + tan^2 A) + (cot^2 A)/(1 + cot^2 A) = 1

Exercise 11.1 | Q 46 | Page 45

Prove the following trigonometric identities.

(cot A - cos A)/(cot A + cos A) = (cosec A - 1)/(cosec A + 1)

Exercise 11.1 | Q 47.1 | Page 45

Prove the following trigonometric identities.

(1 + cos theta + sin theta)/(1 + cos theta - sin theta) = (1 + sin theta)/cos theta

Exercise 11.1 | Q 47.2 | Page 45

Prove the following trigonometric identities.

(sin theta - cos theta + 1)/(sin theta + cos theta - 1) = 1/(sec theta - tan theta)

Exercise 11.1 | Q 47.3 | Page 45

Prove the following trigonometric identities.

(cos theta - sin theta + 1)/(cos theta + sin theta - 1) = cosec theta  + cot theta

Exercise 11.1 | Q 48 | Page 45

Prove the following trigonometric identities.

1/(sec A + tan A) - 1/cos A = 1/cos A - 1/(sec A - tan A)

Exercise 11.1 | Q 49 | Page 45

Prove the following trigonometric identities

tan2 A + cot2 A = sec2 A cosec2 A − 2

Exercise 11.1 | Q 50 | Page 45

Prove the following trigonometric identities.

(1 - tan^2 A)/(cot^2 A -1) = tan^2 A

Exercise 11.1 | Q 51 | Page 45

Prove the following trigonometric identities.

1 + cot^2 theta/(1 + cosec theta) = cosec theta

Exercise 11.1 | Q 51 | Page 45

Prove the following trigonometric identities.

1 + cot^2 theta/(1 + cosec theta) = cosec theta

Exercise 11.1 | Q 52 | Page 45

Prove the following trigonometric identities.

(cos theta)/(cosec theta + 1) + (cos theta)/(cosec theta - 1) = 2 tan theta

Exercise 11.1 | Q 53 | Page 45

Prove the following trigonometric identities.

(1 + cos theta - sin^2 theta)/(sin theta (1 + cos theta)) = cot theta

Exercise 11.1 | Q 54 | Page 45

Prove the following trigonometric identities.

(tan^3 theta)/(1 + tan^2 theta) + (cot^3 theta)/(1 + cot^2 theta) = sec theta cosec theta - 2 sin theta cos theta

Exercise 11.1 | Q 55 | Page 45

Prove the following trigonometric identities.

if T_n = sin^n theta + cos^n theta, prove that (T_3 - T_5)/T_1 = (T_5 - T_7)/T_3

Exercise 11.1 | Q 56 | Page 45

Prove the following trigonometric identities.

[tan θ + 1/cos θ]^2 + [tan θ - 1/cos θ]^2 = 2((1 + sin^2 θ)/(1 - sin^2 θ))

Exercise 11.1 | Q 57 | Page 45

Prove the following trigonometric identities.

(1/(sec^2 theta - cos theta) + 1/(cosec^2 theta - sin^2 theta)) sin^2 theta cos^2 theta = (1 - sin^2 theta cos^2 theta)/(2 + sin^2 theta + cos^2 theta)

Exercise 11.1 | Q 58 | Page 45

Prove the following trigonometric identities.

((1 + sin theta - cos theta)/(1 + sin theta + cos theta))^2 = (1 - cos theta)/(1 + cos theta)

Exercise 11.1 | Q 59 | Page 45

Prove the following trigonometric identities.

(sec A + tan A − 1) (sec A − tan A + 1) = 2 tan A

Exercise 11.1 | Q 60 | Page 46

Prove the following trigonometric identities.

(1 + cot A − cosec A) (1 + tan A + sec A) = 2

Exercise 11.1 | Q 61 | Page 46

Prove the following trigonometric identities.

(cosec θ − sec θ) (cot θ − tan θ) = (cosec θ + sec θ) ( sec θ cosec θ − 2)

Exercise 11.1 | Q 62 | Page 46

Prove the following trigonometric identities.

(sec A − cosec A) (1 + tan A + cot A) = tan A sec A − cot A cosec A

Exercise 11.1 | Q 63 | Page 46

Prove the following trigonometric identities.

(cos A cosec A - sin A sec A)/(cos A + sin A) = cosec A - sec A

Exercise 11.1 | Q 64 | Page 46

Prove the following trigonometric identities.

sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A + 1) = 1

Exercise 11.1 | Q 65 | Page 46

Prove the following trigonometric identities.

tan A/(1 + tan^2  A)^2 + cot A/((1 + cot^2 A)) = sin A  cos A

Exercise 11.1 | Q 66 | Page 46

Prove the following trigonometric identities

sec4 A(1 − sin4 A) − 2 tan2 A = 1

Exercise 11.1 | Q 67 | Page 46

Prove the following trigonometric identities.

(cot^2 A(sec A - 1))/(1 + sin A) = sec^2 A ((1 - sin A)/(1 + sec A))

Exercise 11.1 | Q 68 | Page 46

Prove the following trigonometric identities.

(1 + cot A + tan A)(sin A - cos A) = sec A/(cosec^2 A) - (cosec A)/sec^2 A = sin A tan A - cos A cot A

Exercise 11.1 | Q 69 | Page 46

Prove the following trigonometric identities.

sin2 A cos2 B − cos2 A sin2 B = sin2 A − sin2 B

Exercise 11.1 | Q 70 | Page 46

Prove the following trigonometric identities.

(cot A + tan B)/(cot B + tan A) = cot A tan B

Exercise 11.1 | Q 71 | Page 46

Prove the following trigonometric identities.

(tan A + tan B)/(cot A + cot B) = tan A tan B

Exercise 11.1 | Q 72 | Page 46

Prove the following trigonometric identities.

cot^2 A cosec^2B - cot^2 B cosec^2 A = cot^2 A - cot^2 B

Exercise 11.1 | Q 73 | Page 46

Prove the following trigonometric identities.

tan2 A sec2 B − sec2 A tan2 B = tan2 A − tan2 B

Exercise 11.1 | Q 74 | Page 46

Prove the following trigonometric identities

If x = a sec θ + b tan θ and y = a tan θ + b sec θ, prove that x2 − y2 = a2 − b2

Exercise 11.1 | Q 75 | Page 46

if x/a cos theta + y/b sin theta = 1 and x/a sin theta - y/b cos theta = 1 prove that x^2/a^2 + y^2/b^2  = 2

Exercise 11.1 | Q 76 | Page 46

if cosec theta - sin theta = a^3, sec theta - cos theta = b^3 prove that a^2 b^2 (a^2 + b^2) = 1

Exercise 11.1 | Q 77 | Page 46

if a cos^3 theta + 3a cos theta sin^2 theta = m, a sin^3 theta + 3 a cos^2 theta sin theta = nProve that (m + n)^(2/3) + (m - n)^(2/3)

Exercise 11.1 | Q 78 | Page 47

Prove the following trigonometric identities.

if x = a cos^3 theta, y = b sin^3 theta " prove that " (x/a)^(2/3) + (y/b)^(2/3) = 1

Exercise 11.1 | Q 79 | Page 47

If 3 sin θ + 5 cos θ = 5, prove that 5 sin θ – 3 cos θ = ± 3.

Exercise 11.1 | Q 80 | Page 47

If a cos θ + b sin θ = m and a sin θ – b cos θ = n, prove that a2 + b2 = m2 + n2

Exercise 11.1 | Q 81 | Page 47

If cos θ + cot θ = m and cosec θ – cot θ = n, prove that mn = 1

Exercise 11.1 | Q 82 | Page 47

Prove the following trigonometric identities.

if cos A + cos2 A = 1, prove that sin2 A + sin4 A = 1

Exercise 11.1 | Q 83.1 | Page 47

Prove that: sqrt((sec theta - 1)/(sec theta + 1)) + sqrt((sec theta + 1)/(sec theta - 1)) = 2 cosec theta

Exercise 11.1 | Q 83.2 | Page 47

Prove that

sqrt((1 + sin θ)/(1 - sin θ)) + sqrt((1 - sin θ)/(1 + sin θ)) = 2 sec θ

Exercise 11.1 | Q 83.3 | Page 47

Prove that sqrt((1 + cos theta)/(1 - cos theta)) + sqrt((1 - cos theta)/(1 + cos theta)) = 2 cosec theta

Exercise 11.1 | Q 83.4 | Page 47

Prove that (sec theta - 1)/(sec theta + 1) = ((sin theta)/(1 + cos theta))^2

Exercise 11.1 | Q 84 | Page 47

If cos θ + cos2 θ = 1, prove that sin12 θ + 3 sin10 θ + 3 sin8 θ + sin6 θ + 2 sin4 θ + 2 sin2 θ − 2 = 1

Exercise 11.1 | Q 85 | Page 47

Given that:
(1 + cos α) (1 + cos β) (1 + cos γ) = (1 − cos α) (1 − cos α) (1 − cos β) (1 − cos γ)

Show that one of the values of each member of this equality is sin α sin β sin γ

Exercise 11.1 | Q 86 | Page 47

If sin θ + cos θ = x, prove that  sin^6 theta + cos^6 theta = (4- 3(x^2 - 1)^2)/4

Exercise 11.1 | Q 87 | Page 47

If x = a sec θ cos ϕ, y = b sec θ sin ϕ and z c tan θ, show that x^2/a^2 + y^2/b^2 - x^2/c^2 = 1

Exercise 11.2 [Page 54]

### RD Sharma solutions for Class 10 Maths Chapter 11 Trigonometric Identities Exercise 11.2 [Page 54]

Exercise 11.2 | Q 1 | Page 54

if cos theta = 4/5 find all other trigonometric ratios of angles θ

Exercise 11.2 | Q 2 | Page 54

if sin theta = 1/sqrt2  find all other trigonometric ratios of angle θ.

Exercise 11.2 | Q 3 | Page 54

if tan theta = 1/sqrt2 find the value of (cosec^2 theta - sec^2 theta)/(cosec^2 theta + cot^2 theta)

Exercise 11.2 | Q 4 | Page 54

if tan theta = 3/4, find the value of (1 - cos theta)/(1 +cos theta)

Exercise 11.2 | Q 5 | Page 54

if tan theta = 12/5 find the value of (1 + sin theta)/(1 -sin theta)

Exercise 11.2 | Q 6 | Page 54

if cot theta = 1/sqrt3 find the value of (1 - cos^2 theta)/(2 - sin^2 theta)

Exercise 11.2 | Q 7 | Page 54

if cosec A = sqrt2 find the value of (2 sin^2 A + 3 cot^2 A)/(4(tan^2 A - cos^2 A))

Exercise 11.2 | Q 8 | Page 54

if cot theta = sqrt3 find the value of (cosec^2 theta + cot^2 theta)/(cosec^2 theta - sec^2 theta)

Exercise 11.2 | Q 9 | Page 54

if 3 cos theta = 1, find the value of (6 sin^2 theta + tan^2 theta)/(4 cos theta)

Exercise 11.2 | Q 10 | Page 54

if sqrt3 tan theta = 3 sin theta find the value of sin^2 theta - cos^2 theta

Exercise 11.3 [Pages 55 - 56]

### RD Sharma solutions for Class 10 Maths Chapter 11 Trigonometric Identities Exercise 11.3 [Pages 55 - 56]

Exercise 11.3 | Q 1 | Page 55

Define an identity.

Exercise 11.3 | Q 2 | Page 55

What is the value of (1 − cos2 θ) cosec2 θ?

Exercise 11.3 | Q 3 | Page 55

What is the value of (1 + cot2 θ) sin2 θ?

Exercise 11.3 | Q 4 | Page 55

What is the value of $\sin^2 \theta + \frac{1}{1 + \tan^2 \theta}$

Exercise 11.3 | Q 5 | Page 55

If sec θ + tan θ = x, write the value of sec θ − tan θ in terms of x.

Exercise 11.3 | Q 6 | Page 55

If cosec θ − cot θ = α, write the value of cosec θ + cot α.

Exercise 11.3 | Q 7 | Page 55

Write the value of cosec2 (90° − θ) − tan2 θ.

Exercise 11.3 | Q 8 | Page 55

Write the value of sin A cos (90° − A) + cos A sin (90° − A).

Exercise 11.3 | Q 9 | Page 55

Write the value of $\cot^2 \theta - \frac{1}{\sin^2 \theta}$

Exercise 11.3 | Q 10 | Page 55

If x = a sin θ and y = b cos θ, what is the value of b2x2 + a2y2?

Exercise 11.3 | Q 11 | Page 55

If $\sin \theta = \frac{4}{5}$ what is the value of cotθ + cosecθ?

Exercise 11.3 | Q 12 | Page 55

What is the value of 9cot2 θ − 9cosec2 θ?

Exercise 11.3 | Q 13 | Page 55

What is the value of $6 \tan^2 \theta - \frac{6}{\cos^2 \theta}$

Exercise 11.3 | Q 14 | Page 55

What is the value of $\frac{\tan^2 \theta - \sec^2 \theta}{\cot^2 \theta - {cosec}^2 \theta}$

Exercise 11.3 | Q 15 | Page 55

What is the value of (1 + tan2 θ) (1 − sin θ) (1 + sin θ)?

Exercise 11.3 | Q 16 | Page 55

If $\cos A = \frac{7}{25}$  find the value of tan A + cot A.

Exercise 11.3 | Q 17 | Page 55

If $\sin \theta = \frac{1}{3}$ then find the value of 2cot2 θ + 2.

Exercise 11.3 | Q 18 | Page 55

If $\sin \theta = \frac{1}{3}$ then find the value of 9tan2 θ + 9.

Exercise 11.3 | Q 19 | Page 55

If sec2 θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.

Exercise 11.3 | Q 20 | Page 55

If cosec2 θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ.

Exercise 11.3 | Q 21 | Page 55

If sin2 θ cos2 θ (1 + tan2 θ) (1 + cot2 θ) = λ, then find the value of λ.

Exercise 11.3 | Q 22 | Page 55

If 5x = sec θ and $\frac{5}{x} = \tan \theta$find the value of $5\left( x^2 - \frac{1}{x^2} \right)$

Exercise 11.3 | Q 23 | Page 55

If cosec θ = 2x and $5\left( x^2 - \frac{1}{x^2} \right)$ $2\left( x^2 - \frac{1}{x^2} \right)$

Exercise 11.3 | Q 24.1 | Page 56

The value of  $\sin \theta$ is $x + \frac{1}{x}$ where 'x'  is a positive real number .

Exercise 11.3 | Q 24.2 | Page 56

$\cos \theta = \frac{a^2 + b^2}{2ab}$where a and b are two distinct numbers such that ab > 0.

• True

• False

Exercise 11.3 | Q 24.3 | Page 56

The value of  $\cos^2 23 - \sin^2 67$  is positive .

Exercise 11.3 | Q 24.4 | Page 56

The value of the expression $\sin {80}^° - \cos {80}^°$

Exercise 11.3 | Q 24.5 | Page 56

The value of sin θ+cos θ is always greater than 1 .

Exercise 11.4 [Pages 56 - 59]

### RD Sharma solutions for Class 10 Maths Chapter 11 Trigonometric Identities Exercise 11.4 [Pages 56 - 59]

Exercise 11.4 | Q 1 | Page 56

If sec θ + tan θ = x, then sec θ =

• $\frac{x^2 + 1}{x}$

• $\frac{x^2 + 1}{2x}$

• $\frac{x^2 - 1}{2x}$

• $\frac{x^2 - 1}{x}$

Exercise 11.4 | Q 2 | Page 56

If $sec\theta + tan\theta = x$ then $tan\theta =$

• $\frac{x^2 + 1}{x}$

• $\frac{x^2 - 1}{x}$

• $\frac{x^2 + 1}{2x}$

• $\frac{x^2 - 1}{2x}$

Exercise 11.4 | Q 3 | Page 56

$\frac{x^2 - 1}{2x}$ is equal to

•  sec θ + tan θ

•  sec θ − tan θ

•  sec2 θ + tan2 θ

• sec2 θ − tan2 θ

Exercise 11.4 | Q 4 | Page 56

The value of $\sqrt{\frac{1 + \cos \theta}{1 - \cos \theta}}$

•  cot θ − cosec θ

•  cosec θ + cot θ

• cosec2 θ + cot2 θ

•  (cot θ + cosec θ)2

Exercise 11.4 | Q 5 | Page 56

sec4 A − sec2 A is equal to

• tan2 A − tan4 A

• tan4 A − tan2 A

• tan4 A + tan2 A

•  tan2 A + tan4 A

Exercise 11.4 | Q 6 | Page 56

cos4 A − sin4 A is equal to ______.

• 2 cos2 A + 1

• 2 cos2 A − 1

• 2 sin2 A − 1

• 2 sin2 A + 1

Exercise 11.4 | Q 7 | Page 57

$\frac{\sin \theta}{1 + \cos \theta}$is equal to

• $\frac{\sin \theta}{1 + \cos \theta}$

• $\frac{1 - \cos \theta}{\cos \theta}$

• $\frac{1 - \cos \theta}{\cos \theta}$

• $\frac{1 - \sin \theta}{\cos \theta}$

Exercise 11.4 | Q 8 | Page 57

$\frac{1 - \sin \theta}{\cos \theta}$ is equal to

•  0

• 1

• sin θ + cos θ

• sin θ − cos θ

Exercise 11.4 | Q 9 | Page 57

The value of (1 + cot θ − cosec θ) (1 + tan θ + sec θ) is

• 1

• 2

• 4

• 0

Exercise 11.4 | Q 10 | Page 57

$\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}$ is equal to

• 2 tan θ

•  2 sec θ

•  2 cosec θ

•  2 tan θ sec θ

Exercise 11.4 | Q 11 | Page 57

(cosec θ − sin θ) (sec θ − cos θ) (tan θ + cot θ) is equal to

• 0

• 1

•  −1

• None of these

Exercise 11.4 | Q 12 | Page 57

If x = a cos θ and y = b sin θ, then b2x2 + a2y2 =

• a2 b2

• ab

• a4 b4

• a2 + b2

Exercise 11.4 | Q 13 | Page 57

If x = a sec θ and y = b tan θ, then b2x2 − a2y2 =

•  ab

• a2 − b2

•  a2 + b2

• a2 b2

Exercise 11.4 | Q 14 | Page 57

$\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}$ is equal to

• 0

• 1

• -1

• 2

Exercise 11.4 | Q 15 | Page 57

2 (sin6 θ + cos6 θ) − 3 (sin4 θ + cos4 θ) is equal to

•  0

•  1

•  −1

• None of these

Exercise 11.4 | Q 16 | Page 57

If a cos θ + b sin θ = 4 and a sin θ − b sin θ = 3, then a2 + b2

•  7

• 12

• 25

• None of these

Exercise 11.4 | Q 17 | Page 57

If cot θ + b cosec θ = p and b cot θ − a cosec θ = q, then p2 − q2

• a2 − b2

• b2 − a2

• a2 + b2

•  b − a

Exercise 11.4 | Q 18 | Page 57

The value of sin2 29° + sin2 61° is

• 1

• 0

•  2 sin2 29°

• 2 cos2 61°

Exercise 11.4 | Q 19 | Page 57

If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then

• $x^2 + y^2 + z^2 = r^2$

• $x^2 + y^2 - z^2 = r^2$

• $x^2 - y^2 + z^2 = r^2$

• $z^2 + y^2 - x^2 = r^2$

Exercise 11.4 | Q 20 | Page 58

If sin θ + sin2 θ = 1, then cos2 θ + cos4 θ =

• −1

• 1

• None of these

Exercise 11.4 | Q 21 | Page 58

If a cos θ + b sin θ = m and a sin θ − b cos θ = n, then a2 + b2 =

• m2 − n2

• m2n2

•  n2 − m2

• m2 + n2

Exercise 11.4 | Q 22 | Page 58

If cos A + cos2 A = 1, then sin2 A + sin4 A =

• −1

• 0

• 1

• None of these

Exercise 11.4 | Q 23 | Page 58

If x = a sec θ cos ϕ, y = b sec θ sin ϕ and z = c tan θ, then$\frac{x^2}{a^2} + \frac{y^2}{b^2}$

• $\frac{z^2}{c^2}$

• $1 - \frac{z^2}{c^2}$

• $\frac{z^2}{c^2} - 1$

• $1 + \frac{z^2}{c^2}$

Exercise 11.4 | Q 24 | Page 58

If a cos θ − b sin θ = c, then a sin θ + b cos θ =

• $\pm \sqrt{a^2 + b^2 + c^2}$

• $\pm \sqrt{a^2 + b^2 - c^2}$

• $\pm \sqrt{c^2 - a^2 - b^2}$

•  None of these

Exercise 11.4 | Q 25 | Page 58

9 sec2 A − 9 tan2 A is equal to

• 1

• 9

• 8

• 0

Exercise 11.4 | Q 26 | Page 58

(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = ______.

• 0

• 1

• 2

• -1

• none of these

Exercise 11.4 | Q 27 | Page 58

(sec A + tan A) (1 − sin A) = ______.

• sec A

• sin A

• cosec A

• cos A

Exercise 11.4 | Q 28 | Page 58

$\frac{1 + \tan^2 A}{1 + \cot^2 A}$is equal to

•  sec2 A

• −1

•  cot2 A

•  tan2 A

Exercise 11.4 | Q 29 | Page 58

If sin $\theta - \cos \theta = 0$  then the value of $\sin^4 \theta + \cos^4 \theta$

• 1

• $- 1$

• $\frac{1}{2}$

• $\frac{1}{4}$

Exercise 11.4 | Q 30 | Page 58

The value of sin ( ${45}^° + \theta) - \cos ( {45}^°- \theta)$ is equal to

• 2 cos $\theta$

• 0

•   2 sin $\theta$

• 1

Exercise 11.4 | Q 31 | Page 58

If ∆ABC is right angled at C, then the value of cos (A + B) is ______.

• 0

• 1

• 1/2

• sqrt(3)/2

Exercise 11.4 | Q 32 | Page 59

If cos  $9\theta$ = sin $\theta$ and  $9\theta$  < 900 , then the value of tan $6 \theta$ is

Exercise 11.4 | Q 33 | Page 59

If  cos ($\alpha + \beta$= 0 , then sin $\left( \alpha - \beta \right)$ can be reduced to

## Solutions for Chapter 11: Trigonometric Identities

Exercise 11.1Exercise 11.2Exercise 11.3Exercise 11.4

## RD Sharma solutions for Class 10 Maths chapter 11 - Trigonometric Identities

Shaalaa.com has the CBSE Mathematics Class 10 Maths CBSE solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. RD Sharma solutions for Mathematics Class 10 Maths CBSE 11 (Trigonometric Identities) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

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Concepts covered in Class 10 Maths chapter 11 Trigonometric Identities are Trigonometry Ratio of Zero Degree and Negative Angles, Trigonometric Ratios in Terms of Coordinates of Point, Angles in Standard Position, Trigonometric Ratios of Complementary Angles, Trigonometric Identities, Trigonometric Table, Heights and Distances, Trigonometric Ratios, Application of Trigonometry, Trigonometric Ratios of Complementary Angles, Trigonometric Identities.

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