If f(x) = tan^–1 √((1 + sin x)/(1 - sin x)), 0 ≤ x ≤ π/2, then f'(π/6) is A. -1/4 B. -1/2 C. 1/4 D. 1/2

Question

If f(x) = tan^–1 \(\sqrt{\cfrac{1+sin\,\text x}{1-sin\,\text x}}\), 0 ≤ x  ≤ π/2, then f'(π/6) is

A. -1/4

B. -1/2

C. 1/4

D. 1/2

Answer 1

Correct option is D. 1/2

f(x) =  tan^–1 \(\sqrt{\cfrac{1+sin\,\text x}{1-sin\,\text x}}\)