Answer
See explanations.
Work Step by Step
Starting from the left hand side, we have
$ LHS= \frac{1/cos(x)}{cos(x)/sin(x)+sin(x)/cos(x)}= \frac{1/cos(x)}{cos(x)/sin(x)+sin(x)/cos(x)}\times\frac{sin(x)cos(x)}{sin(x)cos(x)}=\frac{sin(x)}{cos^2x+sin^2x}=sin(x)=RHS$
Thus, we have verified the identity.
