Question

Let 2A + B and A + 2B be acute angles such that sin(2A + B) = √3/2 and tan(A + 2B) = 1. Find the value of cot(4A − 7B).

Find the value of x for which (sin A + cosec A)² + (cos A + sec A)² = x + tan² A + cot² A

Evaluate the following : (3 sin30° – 4 sin³30°)/(2 sin²50° + 2 cos²50°)

Prove that (cos A + sin A – 1)/(cos A – sin A + 1) = cosec A – cot A

If cotθ + cosθ = p and cotθ – cosθ = q, prove that p² – q² = 4√pq