Differentiate with respect to x: cot-1 ( 1 + cos x / sin x ) The answer given - Maths - Continuity and Differentiability

Question

Differentiate with respect to x:

cot-1 ( 1 + cos x / sin x )

The answer given in the book is : 1/2

Manbar Singh · Accepted Answer

Let y = cot-11 + cos xsin x⇒y = cot-12 cos2x/22 sinx/2
 cosx/2⇒y = cot-1cosx/2sinx/2⇒y = cot-1cotx/2⇒y = x2⇒dydx = 12