Samacheer Kalvi solutions for Business Mathematics and Statistics [English] Class 11 TN Board chapter 4 - Trigonometry [Latest edition]

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 sin² `pi/6` + cosec² `(7pi)/6`  cos² `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) = sin² 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 cos² 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.

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:

cos² 15° – sin² 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:

1. cos(A + B)
2. sin(A – B)
3. 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`.

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 sin² `((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.

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.

The degree measure of `pi/8` is

The radian measure of 37°30′ is:

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

The value of sin 15° is:

The value of sin (-420°)

The value of cos(-480°) is:

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

The value of sin 15° cos 15° is:

The value of sec A sin(270° + A) is:

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

The value of cos² 45° – sin² 45° is:

The value of 1 – 2 sin² 45° is:

The value of 4 cos³ 40° – 3 cos 40° is

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

If sin A = `1/2` then 4 cos³ A – 3 cos A is:

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

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

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

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:

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

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

`sin (cos^-1  3/5)` is

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

If p sec 50° = tan 50° then p is:

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

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°.

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.