​ If y = √(sec x-1/sec x+1) then dy/dx = ? ​A. sec^2x B. 1/2 sec^2 x/2 C. -1/2 cosec^2 x/2 D. none of these

Question

If y = \(\sqrt{\frac{sec\,x-1}{sec\,x+1}}\) then dy/dx = ?

√(sec x-1/sec x+1)

A. sec²x

B. 1/2 sec² x/2

C. -1/2 cosec² x/2

D. none of these

Answer 1

Answer is: B. 1/2 sec² x/2

Given that y = \(\sqrt{\frac{sec\,x-1}{sec\,x+1}}\)

Multiplying by cos x in numerator and denominator, we get

Differentiating with respect to x, we get