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