Answer
The left side of the equation is equivalent to $1$ therefore the given equation is an identity.
Refer to the solution below.
Work Step by Step
\begin{align}
\text{LHS }&= \tan^2{\theta} \cos^2{\theta}+\cot^2{\theta} \sin^2{\theta}\\[3mm]
&= \dfrac{\sin^2{\theta}}{\cos^2{\theta}} \dot \cos^2{\theta} + \dfrac{\cos^2{\theta}}{\sin^2{\theta}} \cdot \sin^2{\theta}\\[3mm]
&= \sin^2{\theta}+\cos^2{\theta} \\[3mm]
& = 1 \\[3mm]
& = \text{ RHS}
\end{align}
