# How do you verify the identity 2-sec^2z=1-tan^2z?

##### 1 Answer
Jan 7, 2017

Consider the pythagorean identity ${\tan}^{2} \theta + 1 = {\sec}^{2} \theta$.

Then ${\tan}^{2} \theta = {\sec}^{2} \theta - 1$. Rewrite the starting identity in terms of secant.

$2 - {\sec}^{2} z = 1 - \left({\sec}^{2} z - 1\right)$

$2 - {\sec}^{2} z = 1 - {\sec}^{2} z + 1$

$2 - {\sec}^{2} z = 2 - {\sec}^{2} z$

$L H S = R H S$

Identity proved!

Hopefully this helps!