# How do you rewrite sec^2 (tan^{-1} x) in terms of x?

Oct 24, 2014

Let

$\theta = {\tan}^{- 1} x \Leftrightarrow \tan \theta = x$.

So,

${\sec}^{2} \left({\tan}^{- 1} x\right) = {\sec}^{2} \theta = 1 + {\tan}^{2} \theta = 1 + {x}^{2}$.

I hope that this was helpful.