Answer
$\csc A\sin 2A-\sec A=\cos 2A\sec A$
Work Step by Step
Start with the left side:
$\csc A\sin 2A-\sec A$
Rewrite in terms of sine and cosine:
$=\frac{1}{\sin A}*2\sin A\cos A-\frac{1}{\cos A}$
Simplify:
$=2\cos A-\frac{1}{\cos A}$
$=\frac{2\cos^2 A}{\cos A}-\frac{1}{\cos A}$
$=\frac{2\cos^2 A-1}{\cos A}$
$=\frac{\cos 2A}{\cos A}$
$=\cos 2A\sec A$
Since this equals the right side, the identity has been proven.
