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).

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

Prove that : (1 + 1/tan² θ)(1 + 1/cot² θ) = 1/(sin² θ – sin⁴ θ)

Prove that : √(sec²θ + cosec²θ) = tan θ + cot θ