Answer
See explanations.
Work Step by Step
Step 1. Using the Sum-to- Product Formulas, we have
$LHS=\frac{2cos(\frac{3x+5x}{2})cos(\frac{3x-5x}{2})}{-2sin(\frac{3x+5x}{2})sin(\frac{3x-5x}{2})}=\frac{cos(4x)cos(x)}{sin(4x)sin(x)}$
Step 2. We have
$RHS=cot(x)cot(4x)=\frac{cos(x)}{sin(x)}\times\frac{cos(4x)}{sin(4x)}$
Step 3. Since $LHS=RHS$, we verified the identity.
