Answer
False.
It is a conditional equation. In an identity the equation is true for any $θ$ in the domain of the equation.
Work Step by Step
Test another value of $θ$
$sin^2θ+cos^2θ=1+tan^2θ$
$sin^2(60°)+cos^2(60°)=1+tan^2(60°)$
$\frac{3}{4}+\frac{1}{4}=1+3$
$1=4$ False.