Answer
See explanations.
Work Step by Step
Step 1. $LHS=\frac{1/cos(x)}{cos(x)/sin(x)+sin(x)/cos(x)}=\frac{sin(x)}{cos^2(x)+sin^2(x)}=\frac{sin(x)}{1}$
Step 2. $RHS=sin(x)=\frac{sin(x)}{1}$
Step 3. Since $LHS=RHS$, we verified the identity.