Answer
As left side transforms into right side, hence given identity-
$ \frac{\cos x + 1}{\cot x}$ = $\sin x + \tan x $ is true.
Work Step by Step
Given identity is-
$ \frac{\cos x + 1}{\cot x}$ = $\sin x + \tan x $
Taking L.S.
$ \frac{\cos x + 1}{\cot x}$
= $ \frac{\cos x + 1}{\frac{\cos x}{\sin x}}$
{Using ratio identity for $\cot x$}
= $ \frac{(\cos x + 1) \sin x}{\cos x}$
= $ \frac{\sin x \cos x + \sin x}{\cos x}$
= $ \frac{\sin x \cos x}{\cos x} + \frac{\sin x}{\cos x}$
= $\sin x + \tan x $
= R.S.
As left side transforms into right side, hence given identity-
$ \frac{\cos x + 1}{\cot x}$ = $\sin x + \tan x $ is true.
