# How do you verify the identity tan^2theta+4=sec^2theta+3?

we use the identity $\text{ } 1 + {\tan}^{2} \theta = {\sec}^{2} \theta$
$\text{so taking the "LHS " } {\tan}^{2} \theta + 4 = \textcolor{b l u e}{\left({\tan}^{2} \theta + 1\right)} + 3$
$= \textcolor{b l u e}{{\sec}^{2} \theta} + 3$