Answer
The left hand side is equivalent to $\cot{\theta}$ so the given equation is an identity.
Refer to the solution below.
Work Step by Step
Recall:
(1) $\csc{\theta}= \dfrac{1}{\sin{\theta}} $
(2) $\cot{\theta} = \dfrac{\cos{\theta}}{\sin{\theta}}$
Thus, working on the left hand side (LHS) of the given equation using the definitions above gives:
\begin{align*}
\csc{\theta} \cdot \cos{\theta} &= \dfrac{1}{\sin{\theta}} \cdot \cos{\theta}\\\\ &= \dfrac{\cos{\theta}}{\sin{\theta}}\\\\
&=\cot{\theta}\end{align*}
$\therefore \text{ LHS }= \text{ RHS}$
