HSC Arts Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

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

If x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)`. find the value of xy + yz + zx

Prove that sin(A + B) sin(A – B) = sin²A – sin²B

Prove that cos(A + B) cos(A – B) = cos²A – sin²B = cos²B – sin²A