# Prove that sec^2x(1-cos^2x)=tan^2x?

Nov 24, 2016

#### Explanation:

${\sec}^{2} x \left(1 - {\cos}^{2} x\right)$

= ${\sec}^{2} x - {\sec}^{2} x \times {\cos}^{2} x$

= ${\sec}^{2} x - \frac{1}{\cos} ^ 2 x \times {\cos}^{2} x$

= $1 + {\tan}^{2} x - \frac{1}{\cancel{{\cos}^{2} x}} \times \cancel{{\cos}^{2} x}$

= $1 + {\tan}^{2} x - 1$

= ${\tan}^{2} x$