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