# How do you prove that sec^2x+csc^2x=1 is not an identity?

Nov 12, 2016

${\sec}^{2} x + {\csc}^{2} x = \frac{1}{{\sin}^{2} x {\cos}^{2} x}$

#### Explanation:

Since $\sec x = \frac{1}{\cos} x$ and $\csc x = \frac{1}{\sin} x$, you will get:

${\sec}^{2} x + {\csc}^{2} x = \frac{1}{\cos} ^ 2 x + \frac{1}{\sin} ^ 2 x$

$= \frac{{\sin}^{2} x + {\cos}^{2} x}{{\sin}^{2} x {\cos}^{2} x}$

$= \frac{1}{{\sin}^{2} x {\cos}^{2} x}$