#### Chapters

Chapter 2: Algebra

Chapter 3: Analytical Geometry

Chapter 4: Trigonometry

Chapter 5: Differential Calculus

Chapter 6: Applications of Differentiation

Chapter 7: Financial Mathematics

Chapter 8: Descriptive Statistics and Probability

Chapter 9: Correlation and Regression Analysis

Chapter 10: Operations Research

## Chapter 4: Trigonometry

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 4 TrigonometryExercise 4.1 [Pages 80 - 81]

**Convert the following degree measure into radian measure.**

60°

**Convert the following degree measure into radian measure.**

150°

**Convert the following degree measure into radian measure.**

240°

**Convert the following degree measure into radian measure.**

- 320°

**Find the degree measure corresponding to the following radian measure.**

`pi/8`

**Find the degree measure corresponding to the following radian measure.**

`(9pi)/5`

**Find the degree measure corresponding to the following radian measure.**

-3

**Find the degree measure corresponding to the following radian measure.**

`(11pi)/18`

**Determine the quadrant in which the following degree lie.**

380°

**Determine the quadrant in which the following degree lie.**

-140°

**Determine the quadrant in which the following degree lie.**

1195°

**Find the values of the following trigonometric ratio.**

sin 300°

**Find the values of the following trigonometric ratio.**

cos (-210°)

**Find the values of the following trigonometric ratio.**

sec 390°

**Find the values of the following trigonometric ratio.**

tan(-855°)

**Find the values of the following trigonometric ratio.**

cosec 1125°

**Prove that:**

tan(-225°) cot(-405°) – tan(-765°) cot(675°) = 0.

**Prove that:**

2 sin^{2} `pi/6` + cosec^{2 }`(7pi)/6` cos^{2} `pi/3 = 3/2`

**Prove that:**

`sec((3pi)/2 - theta) sec(theta - (5pi)/2) + tan((5pi)/2 + theta) tan(theta - (5pi)/2)` = - 1

If A, B, C, D are angles of a cyclic quadrilateral, prove that: cos A + cos B + cos C + cos D = 0.

Prove that:

`(sin(180^circ - theta)cos(90^circ + theta)tan(270^circ - theta)cot(360^circ - theta))/(sin(360^circ - theta)cos(360^circ + theta)sin(270^circ - theta)cosec (-theta))` = -1

**Prove that:**

`sin theta * cos theta {sin(pi/2 - theta) * "cosec" theta + cos (pi/2 - theta) * sec theta}` = 1

Prove that: cos 510° cos 330° + sin 390° cos 120° = -1.

Prove that:

tan(π + x) cot(x – π) – cos(2π – x) cos(2π + x) = sin^{2 }x.

Prove that:

`(sin(180^circ + "A")cos(90^circ - "A")tan(270^circ - "A"))/(sec(540^circ - "A") cos(360^circ + "A") "cosec"(270^circ + "A"))` = - sin A cos^{2} A.

If sin θ = `3/5`, tan φ = `1/2 and pi/2` < θ < π < φ < `(3pi)/2,`, then find the value of 8 tan θ – `sqrt5` sec φ.

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 4 TrigonometryExercise 4.2 [Pages 84 - 85]

**Find the value of the following:**

cosec 15º

**Find the value of the following:**

sin (-105°)

**Find the value of the following:**

cot 75°

**Find the value of the following:**

sin 76° cos 16° – cos 76° sin 16°

**Find the value of the following:**

`sin pi/4 cos pi/12 + cos pi/4 sin pi/12`

**Find the value of the following:**

cos 70° cos 10° – sin 70° sin 10°

**Find the value of the following:**

cos^{2} 15° – sin^{2} 15°

If sin A = `3/5`, 0 < A < `pi/2` and cos B = `(-12)/13`, π < B < `(3pi)/2`, find the values of the following:

- cos(A + B)
- sin(A – B)
- tan(A – B)

If cos A = `13/14` and cos B = `1/7` where A, B are acute angles prove that A – B = `pi/3`

Prove that 2 tan 80° = tan 85° – tan 5°.

If cot α = `1/2`, sec β = `(-5)/3`, where π < α < `(3pi)/2 and pi/2` < β < π, find the value of tan(α + β). State the quadrant in which α + β terminates.

If A + B = 45°, prove that (1 + tan A) (1 + tan B) = 2 and hence deduce the value of tan 22`1/2`.

Prove that:

sin(A + 60°) + sin(A – 60°) = sin A.

Prove that:

tan 4A tan 3A tan A + tan 3A + tan A – tan 4A = 0

If tan θ = 3 find tan 3θ

If sin A = `12/13`, find sin 3A.

If sin A = `3/5`, find the values of cos 3A and tan 3A.

Prove that `(sin ("B - C"))/(cos "B" cos "C") + (sin ("C - A"))/(cos "C" cos "A") + (sin ("A - B"))/(cos "A" cos "B")` = 0

If tan A – tan B = x and cot B – cot A = y prove that cot(A – B) = `1/x + 1/y`.

If sin α + sin β = a and cos α + cos β = b, then prove that cos(α – β) = `(a^2 + b^2 - 2)/2`

Find the value of tan `pi/8`.

If tan α = `1/7`, sin β = `1/sqrt10`. Prove that α + 2β = `pi/4` where 0 < α < `pi/2` and 0 < β < `pi/2`.

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 4 TrigonometryExercise 4.3 [Pages 88 - 89]

**Express the following as the sum or difference of sine or cosine:**

`sin "A"/8 sin (3"A")/8`

**Express the following as the sum or difference of sine or cosine:**

cos(60° + A) sin(120° + A)

**Express the following as the sum or difference of sine or cosine:**

`cos (7"A")/3 sin (5"A")/3`

**Express the following as the sum or difference of sine or cosine:**

cos 7θ sin 3θ

**Express the following as the product of sine and cosine.**

sin A + sin 2A

**Express the following as the product of sine and cosine.**

cos 2A + cos 4A

**Express the following as the product of sine and cosine.**

sin 6θ – sin 2θ

**Express the following as the product of sine and cosine.**

cos 2θ – cos θ

Prove that:

cos 20° cos 40° cos 80° = `1/8`

Prove that:

tan 20° tan 40° tan 80° = `sqrt3`.

Prove that:

(cos α – cos β)^{2} + (sin α – sin β)^{2} = 4 sin^{2} `((alpha - beta)/2)`

Prove that:

sin A sin(60° + A) sin(60° – A) = `1/4` sin 3A

Prove that:

sin (A – B) sin C + sin (B – C) sin A + sin(C – A) sin B = 0

Prove that:

2 cos `pi/13` cos \[\frac{9\pi}{13} + \text{cos} \frac{3\pi}{13} + \text{cos} \frac{5\pi}{13}\] = 0

Prove that:

`(cos 2"A" - cos 3"A")/(sin "2A" + sin "3A") = tan "A"/2`

Prove that:

`(cos 7"A" +cos 5"A")/(sin 7"A" −sin 5"A")` = cot A

Prove that cos 20° cos 40° cos 60° cos 80° = `3/16`.

Evaluate-

cos 20° + cos 100° + cos 140°

Evaluate:

sin 50° – sin 70° + sin 10°

If cos A + cos B = `1/2` and sin A + sin B = `1/4`, prove that tan `(("A + B")/2) = 1/2`

If sin(y + z – x), sin(z + x – y), sin(x + y – z) are in A.P, then prove that tan x, tan y and tan z are in A.P.

If cosec A + sec A = cosec B + sec B prove that cot`(("A + B"))/2` = tan A tan B.

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 4 TrigonometryExercise 4.4 [Page 92]

**Find the principal value of the following:**

`sin^-1 (- 1/2)`

**Find the principal value of the following:**

tan^{-1} (-1)

**Find the principal value of the following:**

cosec^{-1} (2)

**Find the principal value of the following:**

`sec^-1 (-sqrt2)`

Prove that:

2 tan^{-1 }(x) = `sin^-1 ((2x)/(1 + x^2))`

Prove that:

`tan^-1 (4/3) + tan^-1 (1/7) = pi/4`

Show that `tan^-1 (1/2) + tan^-1 (2/11) = tan^-1 (3/4)`

Solve `tan^-1 2x + tan^-1 3x = pi/4`

Solve: tan^{-1} (x + 1) + tan^{-1} (x – 1) = `tan^-1 (4/7)`

Evaluate:

`cos[tan^-1 (3/4)]`

Evaluate: sin`[1/2 cos^-1 (4/5)]`

Evaluate: `cos (sin^-1 (4/5) + sin^-1 (12/13))`

Prove that `tan^-1 (m/n) - tan^-1 ((m - n)/(m + n)) = pi/4`

Show that `sin^-1 (- 3/5) - sin^-1 (- 8/17) = cos^-1 (84/85)`

Express `tan^-1 [(cos x)/(1 - sin x)], - pi/2 < x < (3pi)/2` in the simplest form.

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 4 TrigonometryExercise 4.5 [Pages 92 - 94]

#### Choose the correct answer

The degree measure of `pi/8` is

20°60′

22°30′

22°60′

20°30′

The radian measure of 37°30′ is:

`(5pi)/24`

`(3pi)/24`

`(7pi)/24`

`(9pi)/24`

If tan θ = `1/sqrt5` and θ lies in the first quadrant then cos θ is:

`1/sqrt6`

`(-1)/sqrt6`

`sqrt5/sqrt6`

`(-sqrt5)/sqrt6`

The value of sin 15° is:

`(sqrt3 + 1)/(2sqrt2)`

`(sqrt3 - 1)/(2sqrt2)`

`sqrt3/sqrt2`

`(sqrt3)/(2sqrt2)`

The value of sin (-420°)

`sqrt3/2`

`- sqrt3/2`

`1/2`

`- 1/2`

The value of cos(-480°) is:

`sqrt3`

`- sqrt3/2`

`1/2`

`(-1)/2`

The value of sin 28° cos 17° + cos 28° sin 17°

`1/sqrt2`

1

`(-1)/sqrt2`

0

The value of sin 15° cos 15° is:

1

`1/2`

`sqrt3/2`

`1/4`

The value of sec A sin(270° + A) is:

-1

cos

^{2}Asec

^{2}A1

If sin A + cos A = 1 then sin 2A is equal to:

1

2

0

\[\frac{1}{2}\]

The value of cos^{2} 45° – sin^{2} 45° is:

`sqrt3/2`

\[\frac{1}{2}\]

0

`1/sqrt1`

The value of 1 – 2 sin^{2} 45° is:

1

`1/2`

`1/4`

0

The value of 4 cos^{3} 40° – 3 cos 40° is

`sqrt3/2`

`- 1/2`

`1/2`

`1/sqrt2`

The value of `(2 tan 30^circ)/(1 + tan^2 30^circ)` is:

`1/2`

`1/sqrt3`

`sqrt3/2`

`sqrt3`

If sin A = `1/2` then 4 cos^{3} A – 3 cos A is:

1

0

`sqrt3/2`

`1/sqrt2`

The value of `(3 tan 10^circ - tan^3 10^circ)/(1 - 3 tan^2 10^circ)` is:

`1/sqrt3`

`1/2`

`sqrt3/2`

`1/sqrt2`

The value of cosec^{-1} `(2/sqrt3)` is:

`pi/4`

`pi/2`

`pi/3`

`pi/6`

sec^{-1} `(2/3)` + cosec^{-1} `(2/3)`=

`(- pi)/2`

`pi/2`

π

- π

If α and β be between 0 and `pi/2` and if cos(α + β) = `12/13` and sin (α – β) = `3/5` then sin 2α is:

`16/15`

0

`56/65`

`64/65`

If tan A = `1/2` and tan B = `1/3` then tan(2A + B) is equal to:

1

2

3

4

tan`(pi/4 - x)` is:

`((1 + tan x)/(1 - tan x))`

`((1 - tan x)/(1 + tan x))`

1 - tan x

1 + tan x

`sin (cos^-1 3/5)` is

`3/5`

`5/3`

`4/5`

`5/4`

The value of `1/("cosec" (-45^circ))` is:

`(-1)/sqrt2`

`1/sqrt2`

`sqrt2`

`-sqrt2`

If p sec 50° = tan 50° then p is:

cos 50°

sin 50°

tan 50°

sec 50°

`((cos x)/(cosec x)) - sqrt(1 - sin^2x) sqrt(1 - cos^2 x)` is:

cos

^{2}x – sin^{2}xsin

^{2}x – cos^{2}x1

0

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 4 TrigonometryMiscellaneous Problems [Page 94]

Prove that:

`(cos 4x + cos 3x + cos 2x)/(sin 4x + sin 3x + sin 2x)` = cot 3x

Prove that `sqrt3 "cosec" 20^circ - sin 20^circ` = 4

Prove that cot 4x (sin 5x + sin 3x) = cot x(sin 5x - sin 3x).

If tan x = `3/4` and `pi < x < (3pi)/2`, then find the value of sin `x/2` and cos `x/2`.

Prove that `2 sin^2 (3pi)/4 + 2 cos^2 pi/4 + 2 sec^2 pi/3` = 10

Find the value of sin 75°.

Find the value of tan 15°.

If sin A = `1/3`, sin B = `1/4` then find the value of sin (A + B) where A and B are acute angles.

Show that `cos^-1 (12/13) + sin^-1 (3/5) = sin^-1 (56/65)`

If cos (α + β) = `4/5` and sin (α - β) = `5/13` where (α + β) and (α - β) are acute, then find tan 2α.

Express `tan^-1 ((cos x - sin x)/(cos x + sin x))`, 0 < x < π in the simplest form.

## Chapter 4: Trigonometry

## Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide chapter 4 - Trigonometry

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide chapter 4 (Trigonometry) 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 Tamil Nadu Board of Secondary Education Class 11th Business Mathematics and Statistics Answers Guide solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Tamil Nadu Board Samacheer Kalvi textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 11th Business Mathematics and Statistics Answers Guide chapter 4 Trigonometry are Trigonometric Ratios, Trigonometric Ratios of Compound Angles, Transformation Formulae, Inverse Trigonometric Functions.

Using Tamil Nadu Board Samacheer Kalvi Class 11th solutions Trigonometry exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Tamil Nadu Board Samacheer Kalvi Solutions are important questions that can be asked in the final exam. Maximum students of Tamil Nadu Board of Secondary Education Class 11th prefer Tamil Nadu Board Samacheer Kalvi Textbook Solutions to score more in exam.

Get the free view of chapter 4 Trigonometry Class 11th extra questions for Class 11th Business Mathematics and Statistics Answers Guide and can use Shaalaa.com to keep it handy for your exam preparation