#### Answer

$\frac{\sin 2x}{\sin x}=\frac{2}{\sec x}$

#### Work Step by Step

Simplify the left side:
$\frac{\sin 2x}{\sin x}$
$=\frac{2\sin x\cos x}{\sin x}$
$=2\cos x$
Simplify the right side:
$\frac{2}{\sec x}$
$=\frac{2}{\frac{1}{\cos x}}$
$=\frac{2}{\frac{1}{\cos x}}*\frac{\cos x}{\cos x}$
$=2\cos x$
Since the left side and the right side are both equal to $2\cos x$, they are equal to each other, and the identity is proven.