Let f(x) = cos (2tan^-1 sin (cot^-1√(1-x/x)), 0 < x < 1. Then :

Question

Let f(x) = \(cos\left(2tan^{-1}sin\left(cot^{-1}\sqrt{\cfrac{1-x}{x}}\right)\right)\)

f(x) = cos (2tan^-1 sin (co^t-1√(1-x/x)),

0 < x < 1. Then :

(1) (1 – x)² f'(x) – 2(f(x))² = 0 

(2) (1 + x)² f'(x) + 2(f(x))² = 0 

(3) (1 – x)² f'(x) + 2(f(x))² = 0 

(4) (1 + x)² f'(x) – 2(f(x))² = 0

Answer 1

Correct answer is: (3) (1 – x)² f'(x) + 2(f(x))² = 0

 f(x) = \(cos\left(2tan^{-1}sin\left(cot^{-1}\sqrt{\cfrac{1-x}{x}}\right)\right)\)