HSC Science Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions

If sin A = `3/5` and cos B = `9/41 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of sin(A + B)

If sin A = `3/5` and cos B = `9/41, 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of cos(A – B)

Find cos(x − y), given that cos x = `- 4/5` with `pi < x < (3pi)/2`  and sin y = `- 24/25` with `pi < y < (3pi)/2`

Find sin(x – y), given that sin x = `8/17` with 0 < x < `pi/2`, and cos y = `- 24/25`, x < y < `(3pi)/2`

Find the value of cos 105°.

Find the value of sin105°.

Find the value of tan `(7pi)/12`

Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`

Prove that cos(π + θ) = − cos θ

Prove that sin(π + θ) = − sin θ.

Find a quadratic equation whose roots are sin 15° and cos 15°

Expand cos(A + B + C). Hence prove that cos A cos B cos C = sin A sin B cos C + sin B sin C cos A + sin C sin A cos B, if A + B + C = `pi/2`

Prove that sin(45° + θ) – sin(45° – θ) = `sqrt(2) sin θ`

Prove that sin(30° + θ) + cos(60° + θ) = cos θ

If a cos(x + y) = b cos(x − y), show that (a + b) tan x = (a − b) cot y

Prove that sin 105° + cos 105° = cos 45°

Prove that sin 75° – sin 15° = cos 105° + cos 15°

Show that tan 75° + cot 75° = 4

Prove that cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)

Prove that sin(n + 1) θ sin(n – 1) θ + cos(n + 1) θ cos(n – 1)θ = cos 2θ, n ∈ Z