Answer
As left side transforms into right side, hence given identity-
$\sin^{2} x (\cot^{2} x + 1)$ = $1$ is true.
Work Step by Step
Given identity is-
$\sin^{2} x (\cot^{2} x + 1)$ = $1$
Taking L.S.
$\sin^{2} x (\cot^{2} x + 1)$
= $\sin^{2} x . \frac{\cos^{2} x}{\sin^{2} x} + \sin^{2} x$
( Using ratio identity for $\cot^{2} x$)
= $\cos^{2} x + \sin^{2} x$
= 1 (Pythagorean identity)
= R.S.
As left side transforms into right side, hence given identity-
$\sin^{2} x (\cot^{2} x + 1)$ = $1$ is true.
