## Precalculus (6th Edition)

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