Answer
$\frac{\tan\alpha}{\sec\alpha}=\sin\alpha$
Work Step by Step
Start with the left side:
$\frac{\tan\alpha}{\sec\alpha}$
Rewrite everything in terms of sine and cosine:
$=\frac{\frac{\sin\alpha}{\cos\alpha}}{\frac{1}{\cos \alpha}}$
Multiply top and bottom by $\cos\alpha$ and simplify:
$=\frac{\frac{\sin\alpha}{\cos\alpha}*\cos\alpha}{\frac{1}{\cos \alpha}*\cos\alpha}$
$=\frac{\sin\alpha}{1}$
$=\sin\alpha$
Since this equals the right side, the identity has been proven.
