If y(x) = cot^(-1)(√(1+sinx)+√(1-sinx))/(√(1+sinx)-√(1-sinx)),x ∈ (π/2,π), then dy/dx at x = 5π/6 is :

Question

If y(x) = cot^-1(\(\frac{\sqrt{1+sinx}+\sqrt{1-sinx}}{\sqrt{1+sinx}-\sqrt{1-sinx}}\)),x ∈ (π/2,π), then dy/dx at x = 5π/6 is :

cot^-1(√(1+sinx)+√(1-sinx))/(√(1+sinx)-√(1-sinx))

(1) \(-\frac{1}{2}\) 

(2) –1 

(3) \(\frac{1}{2}\)

(4) 0

Answer 1

Option : (1) \(-\frac{1}{2}\) 

cot^-1(√(1+sinx)+√(1-sinx))/(√(1+sinx)-√(1-sinx))