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# RD Sharma solutions for Class 11 Mathematics Textbook chapter 7 - Values of Trigonometric function at sum or difference of angles [Latest edition]

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## Chapter 7: Values of Trigonometric function at sum or difference of angles

Ex. 7.1Ex. 7.2Others

#### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 7 Values of Trigonometric function at sum or difference of angles Exercise 7.1 [Pages 10 - 21]

Ex. 7.1 | Q 1.1 | Page 19

If $\sin A = \frac{4}{5}$ and $\cos B = \frac{5}{13}$, where 0 < A, $B < \frac{\pi}{2}$, find the value of the following:

sin (A + B)

Ex. 7.1 | Q 1.2 | Page 19

If $\sin A = \frac{4}{5}$ and $\cos B = \frac{5}{13}$, where 0 < A, $B < \frac{\pi}{2}$, find the value of the following:
cos (A + B)

Ex. 7.1 | Q 1.3 | Page 19

If $\sin A = \frac{4}{5}$ and $\cos B = \frac{5}{13}$, where 0 < A, $B < \frac{\pi}{2}$, find the value of the following:
sin (A − B)

Ex. 7.1 | Q 1.4 | Page 19

If $\sin A = \frac{4}{5}$ and $\cos B = \frac{5}{13}$, where 0 < A, $B < \frac{\pi}{2}$, find the value of the following:
cos (A − B)

Ex. 7.1 | Q 2.1 | Page 19

If $\sin A = \frac{12}{13}\text{ and } \sin B = \frac{4}{5}$, where $\frac{\pi}{2}$ < A < π and 0 < B < $\frac{\pi}{2}$, find the following:
sin (A + B)

Ex. 7.1 | Q 2.2 | Page 19

If $\sin A = \frac{12}{13}\text{ and } \sin B = \frac{4}{5}$, where $\frac{\pi}{2}$ < A < π and 0 < B < $\frac{\pi}{2}$, find the following:
cos (A + B)

Ex. 7.1 | Q 2.3 | Page 19

If $\sin A = \frac{3}{5}, \cos B = - \frac{12}{13}$, where A and B both lie in second quadrant, find the value of sin (A + B).

Ex. 7.1 | Q 3.1 | Page 10

If $\cos A = - \frac{24}{25}\text{ and }\cos B = \frac{3}{5}$, where π < A < $\frac{3\pi}{2}\text{ and }\frac{3\pi}{2}$< B < 2π, find the following:
sin (A + B)

Ex. 7.1 | Q 3.2 | Page 19

If $\cos A = - \frac{24}{25}\text{ and }\cos B = \frac{3}{5}$, where π < A < $\frac{3\pi}{2}\text{ and }\frac{3\pi}{2}$< B < 2π, find the following:
cos (A + B)

Ex. 7.1 | Q 4 | Page 19

If $\tan A = \frac{3}{4}, \cos B = \frac{9}{41}$, where π < A < $\frac{3\pi}{2}$ and 0 < B <$\frac{\pi}{2}$, find tan (A + B).

Ex. 7.1 | Q 5 | Page 19

If $\sin A = \frac{1}{2}, \cos B = \frac{12}{13}$, where $\frac{\pi}{2}$< A < π and $\frac{3\pi}{2}$ < B < 2π, find tan (A − B).

Ex. 7.1 | Q 6.1 | Page 19

If $\sin A = \frac{1}{2}, \cos B = \frac{\sqrt{3}}{2}$, where $\frac{\pi}{2}$ < A < π and 0 < B < $\frac{\pi}{2}$, find the following:
tan (A + B)

Ex. 7.1 | Q 6.2 | Page 19

If $\sin A = \frac{1}{2}, \cos B = \frac{\sqrt{3}}{2}$, where $\frac{\pi}{2}$ < A < π and 0 < B < $\frac{\pi}{2}$, find the following:
tan (A - B)

Ex. 7.1 | Q 7.1 | Page 19

Evaluate the following:
sin 78° cos 18° − cos 78° sin 18°

Ex. 7.1 | Q 7.2 | Page 19

Evaluate the following:
cos 47° cos 13° − sin 47° sin 13°

Ex. 7.1 | Q 7.3 | Page 19

Evaluate the following:
sin 36° cos 9° + cos 36° sin 9°

Ex. 7.1 | Q 7.4 | Page 19

Evaluate the following:
cos 80° cos 20° + sin 80° sin 20°

Ex. 7.1 | Q 8.1 | Page 19

If $\cos A = - \frac{12}{13}\text{ and }\cot B = \frac{24}{7}$, where A lies in the second quadrant and B in the third quadrant, find the values of the following:
sin (A + B)

Ex. 7.1 | Q 8.2 | Page 19

If $\cos A = - \frac{12}{13}\text{ and }\cot B = \frac{24}{7}$, where A lies in the second quadrant and B in the third quadrant, find the values of the following:
cos (A + B)

Ex. 7.1 | Q 8.3 | Page 19

If $\cos A = - \frac{12}{13}\text{ and }\cot B = \frac{24}{7}$, where A lies in the second quadrant and B in the third quadrant, find the values of the following:
tan (A + B)

Ex. 7.1 | Q 9 | Page 19

Prove that:
$\frac{7\pi}{12} + \cos\frac{\pi}{12} = \sin\frac{5\pi}{12} - \sin\frac{\pi}{12}$

Ex. 7.1 | Q 10 | Page 19

Prove that
$\frac{\tan A + \tan B}{\tan A - \tan B} = \frac{\sin \left( A + B \right)}{\sin \left( A - B \right)}$

Ex. 7.1 | Q 11.1 | Page 19

Prove that

$\frac{\cos 11^\circ + \sin 11^\circ}{\cos 11^\circ - \sin 11^\circ} = \tan 56^\circ$
Ex. 7.1 | Q 11.2 | Page 19

Prove that

$\frac{\cos 9^\circ + \sin 9^\circ}{\cos 9^\circ - \sin 9^\circ} = \tan 54^\circ$
Ex. 7.1 | Q 11.3 | Page 19

Prove that

$\frac{\cos 8^\circ - \sin 8^\circ}{\cos 8^\circ + \sin 8^\circ} = \tan 37^\circ$
Ex. 7.1 | Q 12.1 | Page 19

Prove that:

$\sin\left( \frac{\pi}{3} - x \right)\cos\left( \frac{\pi}{6} + x \right) + \cos\left( \frac{\pi}{3} - x \right)\sin\left( \frac{\pi}{6} + x \right) = 1$

Ex. 7.1 | Q 12.2 | Page 19

Prove that:

$\sin\left( \frac{4\pi}{9} + 7 \right)\cos\left( \frac{\pi}{9} + 7 \right) - \cos\left( \frac{4\pi}{9} + 7 \right)\sin\left( \frac{\pi}{9} + 7 \right) = \frac{\sqrt{3}}{2}$

Ex. 7.1 | Q 12.3 | Page 19

Prove that:

$\sin\left( \frac{3\pi}{8} - 5 \right)\cos\left( \frac{\pi}{8} + 5 \right) + \cos\left( \frac{3\pi}{8} - 5 \right)\sin\left( \frac{\pi}{8} + 5 \right) = 1$

Ex. 7.1 | Q 13 | Page 19

Prove that $\frac{\tan 69^\circ + \tan 66^\circ}{1 - \tan 69^\circ \tan 66^\circ} = - 1$.

Ex. 7.1 | Q 14.1 | Page 20

If $\tan A = \frac{5}{6}\text{ and }\tan B = \frac{1}{11}$, prove that $A + B = \frac{\pi}{4}$.

Ex. 7.1 | Q 14.2 | Page 20

If $\tan A = \frac{m}{m - 1}\text{ and }\tan B = \frac{1}{2m - 1}$, then prove that $A - B = \frac{\pi}{4}$.

Ex. 7.1 | Q 15.1 | Page 20

Prove that:
$\cos^2 45^\circ - \sin^2 15^\circ = \frac{\sqrt{3}}{4}$

Ex. 7.1 | Q 15.2 | Page 20

Prove that:
sin2 (n + 1) A − sin2 nA = sin (2n + 1) A sin A.

Ex. 7.1 | Q 16.1 | Page 20

Prove that: $\frac{\sin \left( A + B \right) + \sin \left( A - B \right)}{\cos \left( A + B \right) + \cos \left( A - B \right)} = \tan A$

Ex. 7.1 | Q 16.2 | Page 20

Prove that:
$\frac{\sin \left( A - B \right)}{\cos A \cos B} + \frac{\sin \left( B - C \right)}{\cos B \cos C} + \frac{\sin \left( C - A \right)}{\cos C \cos A} = 0$

Ex. 7.1 | Q 16.3 | Page 20

Prove that:

$\frac{\sin \left( A - B \right)}{\sin A \sin B} + \frac{\sin \left( B - C \right)}{\sin B \sin C} + \frac{\sin \left( C - A \right)}{\sin C \sin A} = 0$

Ex. 7.1 | Q 16.4 | Page 20

Prove that:
sin2 B = sin2 A + sin2 (A − B) − 2 sin A cos B sin (A − B)

Ex. 7.1 | Q 16.5 | Page 20

Prove that:
cos2 A + cos2 B − 2 cos A cos B cos (A + B) = sin2 (A + B)

Ex. 7.1 | Q 16.6 | Page 20

Prove that:
$\frac{\tan \left( A + B \right)}{\cot \left( A - B \right)} = \frac{\tan^2 A - \tan^2 B}{1 - \tan^2 A \tan^2 B}$

Ex. 7.1 | Q 17.1 | Page 20

Prove that:
tan 8x − tan 6x − tan 2x = tan 8x tan 6x tan 2x

Ex. 7.1 | Q 17.2 | Page 20

Prove that:
$\tan\frac{\pi}{12} + \tan\frac{\pi}{6} + \tan\frac{\pi}{12}\tan\frac{\pi}{6} = 1$

Ex. 7.1 | Q 17.3 | Page 20

Prove that:
tan 36° + tan 9° + tan 36° tan 9° = 1

Ex. 7.1 | Q 17.4 | Page 20

Prove that:
tan 13x − tan 9x − tan 4x = tan 13x tan 9x tan 4x

Ex. 7.1 | Q 18 | Page 20

Prove that:
$\frac{\tan^2 2x - \tan^2 x}{1 - \tan^2 2x \tan^2 x} = \tan 3x \tan x$

Ex. 7.1 | Q 19 | Page 20

Prove that sin2 (n + 1) A − sin2 nA = sin (2n + 1) A sin A.

Ex. 7.1 | Q 20 | Page 20

If tan A = x tan B, prove that
$\frac{\sin \left( A - B \right)}{\sin \left( A + B \right)} = \frac{x - 1}{x + 1}$

Ex. 7.1 | Q 21 | Page 20

If tan (A + B) = x and tan (A − B) = y, find the values of tan 2A and tan 2B.

Ex. 7.1 | Q 22 | Page 20

If cos A + sin B = m and sin A + cos B = n, prove that 2 sin (A + B) = m2 + n2 − 2.

Ex. 7.1 | Q 23 | Page 20

If tan A + tan B = a and cot A + cot B = b, prove that cot (A + B) $\frac{1}{a} - \frac{1}{b}$.

Ex. 7.1 | Q 24 | Page 20

If x lies in the first quadrant and $\cos x = \frac{8}{17}$, then prove that:

$\cos \left( \frac{\pi}{6} + x \right) + \cos \left( \frac{\pi}{4} - x \right) + \cos \left( \frac{2\pi}{3} - x \right) = \left( \frac{\sqrt{3} - 1}{2} + \frac{1}{\sqrt{2}} \right)\frac{23}{17}$

Ex. 7.1 | Q 25 | Page 20

If tan x + $\tan \left( x + \frac{\pi}{3} \right) + \tan \left( x + \frac{2\pi}{3} \right) = 3$, then prove that $\frac{3 \tan x - \tan^3 x}{1 - 3 \tan^2 x} = 1$.

Ex. 7.1 | Q 26 | Page 21

If sin (α + β) = 1 and sin (α − β) $= \frac{1}{2}$, where 0 ≤ α, $\beta \leq \frac{\pi}{2}$, then find the values of tan (α + 2β) and tan (2α + β).

Ex. 7.1 | Q 27 | Page 21

If α, β are two different values of x lying between 0 and 2π, which satisfy the equation 6 cos x + 8 sin x = 9, find the value of sin (α + β).

Ex. 7.1 | Q 28.1 | Page 21

If sin α + sin β = a and cos α + cos β = b, show that

$\sin \left( \alpha + \beta \right) = \frac{2ab}{a^2 + b^2}$

Ex. 7.1 | Q 28.2 | Page 21

If sin α + sin β = a and cos α + cos β = b, show that

$\cos \left( \alpha + \beta \right) = \frac{b^2 - a^2}{b^2 + a^2}$
Ex. 7.1 | Q 29.1 | Page 21

Prove that:
$\frac{1}{\sin \left( x - a \right) \sin \left( x - b \right)} = \frac{\cot \left( x - a \right) - \cot \left( x - b \right)}{\sin \left( a - b \right)}$

Ex. 7.1 | Q 29.2 | Page 21

Prove that:

$\frac{1}{\sin \left( x - a \right) \cos \left( x - b \right)} = \frac{\cot \left( x - a \right) + \tan \left( x - b \right)}{\cos \left( a - b \right)}$

Ex. 7.1 | Q 29.3 | Page 21

Prove that:

$\frac{1}{\cos \left( x - a \right) \cos \left( a - b \right)} = \frac{\tan \left( x - b \right) - \tan \left( x - a \right)}{\sin \left( a - b \right)}$

Ex. 7.1 | Q 30 | Page 21

If sin α sin β − cos α cos β + 1 = 0, prove that 1 + cot α tan β = 0.

Ex. 7.1 | Q 31 | Page 21

If tan α = x +1, tan β = x − 1, show that 2 cot (α − β) = x2.

Ex. 7.1 | Q 32 | Page 21

If angle $\theta$  is divided into two parts such that the tangents of one part is $\lambda$ times the tangent of other, and $\phi$ is their difference, then show that$\sin\theta = \frac{\lambda + 1}{\lambda - 1}\sin\phi$

Ex. 7.1 | Q 33 | Page 21

If $\tan\theta = \frac{\sin\alpha - \cos\alpha}{\sin\alpha + \cos\alpha}$ , then show that $\sin\alpha + \cos\alpha = \sqrt{2}\cos\theta$.

Ex. 7.1 | Q 34 | Page 21

If α and β are two solutions of the equation a tan x + b sec x = c, then find the values of sin (α + β) and cos (α + β).

#### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 7 Values of Trigonometric function at sum or difference of angles Exercise 7.2 [Page 26]

Ex. 7.2 | Q 1.1 | Page 26

Find the maximum and minimum values of each of the following trigonometrical expression:

12 sin x − 5 cos

Ex. 7.2 | Q 1.2 | Page 26

Find the maximum and minimum values of each of the following trigonometrical expression:

12 cos x + 5 sin x + 4

Ex. 7.2 | Q 1.3 | Page 26

Find the maximum and minimum values of each of the following trigonometrical expression:

$5 \cos x + 3 \sin \left( \frac{\pi}{6} - x \right) + 4$

Ex. 7.2 | Q 1.4 | Page 26

Find the maximum and minimum values of each of the following trigonometrical expression:

sin x − cos x + 1

Ex. 7.2 | Q 2.1 | Page 26

Reduce each of the following expressions to the sine and cosine of a single expression:

$\sqrt{3} \sin x - \cos x$

Ex. 7.2 | Q 2.2 | Page 26

Reduce each of the following expressions to the sine and cosine of a single expression:

cos x − sin

Ex. 7.2 | Q 2.3 | Page 26

Reduce each of the following expressions to the sine and cosine of a single expression:

24 cos x + 7 sin

Ex. 7.2 | Q 3 | Page 26

Show that sin 100° − sin 10° is positive.

Ex. 7.2 | Q 4 | Page 26

Prove that $\left( 2\sqrt{3} + 3 \right) \sin x + 2\sqrt{3} \cos x$  lies between $- \left( 2\sqrt{3} + \sqrt{15} \right) \text{ and } \left( 2\sqrt{3} + \sqrt{15} \right)$

#### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 7 Values of Trigonometric function at sum or difference of angles [Pages 26 - 27]

Q 1 | Page 26

If α + β − γ = π and sin2 α +sin2 β − sin2 γ = λ sin α sin β cos γ, then write the value of λ.

Q 2 | Page 26

If x cos θ = y cos $\left( \theta + \frac{2\pi}{3} \right) = z \cos \left( \theta + \frac{4\pi}{3} \right)$then write the value of $\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$

Q 3 | Page 26

Write the maximum and minimum values of 3 cos x + 4 sin x + 5.

Q 4 | Page 26

Write the maximum value of 12 sin x − 9 sin2 x

Q 5 | Page 26

If 12 sin x − 9sin2 x attains its maximum value at x = α, then write the value of sin α.

Q 6 | Page 27

Write the interval in which the value of 5 cos x + 3 cos $\left( x + \frac{\pi}{3} \right) + 3$ lies.

Q 7 | Page 27

If tan (A + B) = p and tan (A − B) = q, then write the value of tan 2B

Q 8 | Page 27

If $\frac{\cos \left( x - y \right)}{\cos \left( x + y \right)} = \frac{m}{n}$  then write the value of tan x tan y

Q 9 | Page 27

If a = b $\cos \frac{2\pi}{3} = c \cos\frac{4\pi}{3}$ then write the value of ab + bc + ca.

Q 10 | Page 27

If A + B = C, then write the value of tan A tan B tan C.

Q 11 | Page 27

If sin α − sin β = a and cos α + cos β = b, then write the value of cos (α + β).

Q 12 | Page 27

If tan $\alpha = \frac{1}{1 + 2^{- x}}$ and $\tan \beta = \frac{1}{1 + 2^{x + 1}}$ then write the value of α + β lying in the interval $\left( 0, \frac{\pi}{2} \right)$

#### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 7 Values of Trigonometric function at sum or difference of angles [Pages 27 - 29]

Q 1 | Page 27

The value of $\sin^2 \frac{5\pi}{12} - \sin^2 \frac{\pi}{12}$

• (a) $\frac{1}{2}$

• (b) $\frac{\sqrt{3}}{2}$

• (c) 1

• (d) 0

Q 2 | Page 27

If A + B + C = π, then sec A (cos B cos C − sin B sin C) is equal to

• (a) 0

• (b) −1

• (c) 1

• (d) None of these

Q 3 | Page 27

tan 20° + tan 40° + $\sqrt{3}$ tan 20° tan 40° is equal to

• (a) $\frac{\sqrt{3}}{4}$

• (b) $\frac{\sqrt{3}}{2}$

• (c) $\sqrt{3}$

• (d) 1

Q 4 | Page 27

If $\tan A = \frac{a}{a + 1}\text{ and } \tan B = \frac{1}{2a + 1}$

• (a) 0

• (b)$\frac{\pi}{2}$

• (c) $\frac{\pi}{3}$

• (d) $\frac{\pi}{4}$

Q 5 | Page 27

If 3 sin x + 4 cos x = 5, then 4 sin x − 3 cos x =

• 0

• 5

• 1

• None of these

Q 6 | Page 27

If in ∆ABC, tan A + tan B + tan C = 6, then cot A cot B cot C =

• 6

• 1

• $\frac{1}{6}$

• None of these

Q 7 | Page 27

tan 3A − tan 2A − tan A =

•  tan 3 A tan 2 A tan A

• −tan 3 A tan 2 A tan A

•  tan A tan 2 A − tan 2 A tan 3 A − tan 3 A tan A

• None of these

Q 8 | Page 27

If A + B + C = π, then $\frac{\tan A + \tan B + \tan C}{\tan A \tan B \tan C}$ is equal to

• tan A tan B tan C

• 0

• 1

• None of these

Q 9 | Page 27

If $\cos P = \frac{1}{7}\text{ and }\cos Q = \frac{13}{14}$, where P and Q both are acute angles. Then, the value of P − Q is

• $\frac{\pi}{6}$

• $\frac{\pi}{3}$

• $\frac{\pi}{4}$

• $\frac{\pi}{12}$

Q 10 | Page 28

If cot (α + β) = 0, sin (α + 2β) is equal to

• sin α

•  cos 2 β

• cos α

• sin 2 α

Q 11 | Page 28
$\frac{\cos 10^\circ + \sin 10^\circ}{\cos 10^\circ - \sin 10^\circ} =$

•  tan 55°

• cot 55°

•  −tan 35°

• −cot 35°

Q 12 | Page 28

The value of $\cos^2 \left( \frac{\pi}{6} + x \right) - \sin^2 \left( \frac{\pi}{6} - x \right)$ is

• $\frac{1}{2} \cos 2 x$

• 0

• $- \frac{1}{2} \cos 2 x$

• $\frac{1}{2}$

Q 13 | Page 28

If tan θ1 tan θ2 = k, then $\frac{\cos \left( \theta_1 - \theta_2 \right)}{\cos \left( \theta_1 + \theta_2 \right)} =$

• $\frac{1 + k}{1 - k}$

• $\frac{1 - k}{1 + k}$

• $\frac{k + 1}{k - 1}$

• $\frac{k - 1}{k + 1}$

Q 14 | Page 28

If sin (π cos x) = cos (π sin x), then sin 2 x =

• $\pm \frac{3}{4}$

• $\pm \frac{4}{3}$

• $\pm \frac{1}{3}$

• none of these

Q 15 | Page 28

If $\tan\theta = \frac{1}{2}$ and $\tan\phi = \frac{1}{3}$, then the value of $\tan\phi = \frac{1}{3}$ is

• $\frac{\pi}{6}$

• $\pi$

• 0

• $\frac{\pi}{4}$

Q 16 | Page 28

The value of cos (36° − A) cos (36° + A) + cos (54° + A) cos (54° − A) is

• sin 2A

• cos 2A

• cos 3A

• sin 3A

Q 17 | Page 28

If tan (π/4 + x) + tan (π/4 − x) = a, then tan2 (π/4 + x) + tan2 (π/4 − x) =

•  a2 + 1

• a2 + 2

• a2 − 2

•  None of these

Q 18 | Page 28

If tan (A − B) = 1 and sec (A + B) = $\frac{2}{\sqrt{3}}$, the smallest positive value of B is

• $\frac{25 \pi}{24}$

• $\frac{19 \pi}{24}$

• $\frac{13\pi}{24}$

• $\frac{11 \pi}{24}$

Q 19 | Page 28

If A − B = π/4, then (1 + tan A) (1 − tan B) is equal to

• 2

• 1

• 0

• 3

Q 20 | Page 28

The maximum value of $\sin^2 \left( \frac{2\pi}{3} + x \right) + \sin^2 \left( \frac{2\pi}{3} - x \right)$ is

• 1/2

• $\frac{3}{2}$

• 1/4

• 3/4

Q 21 | Page 28

If cos (A − B) $= \frac{3}{5}$ and tan A tan B = 2, then

• $\cos A \cos B = \frac{1}{5}$

• $\cos A \cos B = - \frac{1}{5}$

• $\sin A \sin B = - \frac{1}{5}$

• $\sin A \sin B = - \frac{1}{5}$

Q 22 | Page 28

If tan 69° + tan 66° − tan 69° tan 66° = 2k, then k =

• −1

• $\frac{1}{2}$

• $- \frac{1}{2}$

• None of these

Q 23 | Page 29

If $\tan\alpha = \frac{x}{x + 1}$ and $\tan\alpha = \frac{x}{x + 1}$, then $\alpha + \beta$ is equal to

• $\frac{\pi}{2}$

• $\frac{\pi}{3}$

• $\frac{\pi}{6}$

• $\frac{\pi}{4}$

## Chapter 7: Values of Trigonometric function at sum or difference of angles

Ex. 7.1Ex. 7.2Others

## RD Sharma solutions for Class 11 Mathematics Textbook chapter 7 - Values of Trigonometric function at sum or difference of angles

RD Sharma solutions for Class 11 Mathematics Textbook chapter 7 (Values of Trigonometric function at sum or difference of angles) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 11 Mathematics Textbook solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 11 Mathematics Textbook chapter 7 Values of Trigonometric function at sum or difference of angles are Transformation Formulae, Values of Trigonometric Functions at Multiples and Submultiples of an Angle, Sine and Cosine Formulae and Their Applications, 180 Degree Plusminus X Function, 2X Function, 3X Function, Expressing Sin (X±Y) and Cos (X±Y) in Terms of Sinx, Siny, Cosx and Cosy and Their Simple Applications, Concept of Angle, Introduction of Trigonometric Functions, Signs of Trigonometric Functions, Domain and Range of Trigonometric Functions, Trigonometric Functions of Sum and Difference of Two Angles, Trigonometric Equations, Truth of the Identity, Negative Function Or Trigonometric Functions of Negative Angles, 90 Degree Plusminus X Function, Conversion from One Measure to Another, Graphs of Trigonometric Functions.

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