Answer
The left side of the equation is equivalent to $3+\cos^2{\theta}$ therefore the given equation is an identity.
Refer to the solution below.
Work Step by Step
\begin{align}
$\text{LHS } &= 3 \sin^2{\theta} + 4 \cos^2{\theta} \\[3mm]
&= 3 \sin^2{\theta} + 3 \cos^2{\theta}+\cos^2{\theta} \\[3mm]
&= 3(\sin^2{\theta}+\cos^2{\theta})+\cos^2{\theta} \\[3mm]
&= 3(1)+\cos^2{\theta} \\[3mm]
&= 3+\cos^2{\theta} \\[3mm]
&= 3+\cos^2{\theta} \\[3mm]
&= \text{ RHS}
\end{align}
