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