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