Answer
See explanations.
Work Step by Step
Step 1. $LHS=\frac{sin(\alpha) cos(\beta)-cos(\alpha) sin(\beta)}{sin(\alpha) cos(\beta)}=1-\frac{cos(\alpha) sin(\beta)}{sin(\alpha) cos(\beta)}$
Step 2. $RHS=1-\frac{cos(\alpha)}{sin(\alpha)}\times \frac{sin(\beta)}{cos(\beta)}$
Step 3. Since $LHS=RHS$, we verified the identity.
