# How do you prove sec(2x)= ((secx)^2)/(2-(secx)^2)?

Apr 24, 2016

Prove trig expression

#### Explanation:

Apply the trig identities:
sìn^2 x + cos ^2 x = 1
$\cos 2 x = 2 {\cos}^{2} x - 1$
$\sec \left(2 x\right) = \frac{1}{\cos} \left(2 x\right) = \frac{1}{2 {\cos}^{2} x - 1}$
Divide both numerator and denominator by ${\cos}^{2} x$, we get:
$\sec 2 x = \frac{\frac{1}{\cos} ^ 2 x}{2 - \frac{1}{\cos} ^ 2 x} = {\sec}^{2} \frac{x}{2 - {\sec}^{2} x}$