The solution to 2 tan⁻¹(cos x) = tan⁻¹(2 cosec x) is:

The solution to 2 tan⁻¹(cos x) = tan⁻¹(2 cosec x) is:

• A. π/3
• B. π/4
• C. π/6
• D. π/2

Answer: B) π/4

Explanation: Using 2 tan⁻¹(y) = tan⁻¹(2y/(1−y²)). We get 2 cos x / (1 − cos²x) = 2 cosec x. So 2 cos x / sin²x = 2 / sin x. Thus cot x = 1, meaning x = π/4.