If, 2 × sinq × cos(90° − q) = (1/2), such that 0°

Question

If, 2 × sinq × cos(90° − q) = (1/2), such that 0° < q < 90°, then find the value of cot²2q + cos²3q.

Accepted Answer

1/3. cos(90°−q) = sinq, so 2sin²q = 1/2, sin²q = 1/4, sinq = 1/2, q = 30°. Then cot²(60°) + cos²(90°) = (1/√3)² + 0 = 1/3.

If, 2 × sinq × cos(90° − q) = (1/2), such that 0° < q < 90°, then find the value of cot²2q + cos²3q.