# How do you verify the identity sec^2(pi/2-x)-1=cot^2x?

Jan 26, 2017

see below

#### Explanation:

Use the formulas $\sec \left(\frac{\pi}{2} - x\right) = \csc x$ and $1 + {\cot}^{2} x = {\csc}^{2} x$

Therefore,
Left Hand Side:

${\sec}^{2} \left(\frac{\pi}{2} - x\right) - 1 = {\csc}^{2} x - 1 = {\cot}^{2} x =$Right Hand Side