# Question #831dc

Apr 15, 2016

see below

#### Explanation:

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

Use the property ${\sec}^{2} x = {\tan}^{2} x + 1$

LHS=Left hand side. RHS=Right hand side. We start with the left hand side and show that it equals the right hand side.

$L H S = {\sec}^{2} x - 1$

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

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

$= R H S$