# Chapter 5 - Review Exercises - Page 708: 48

See explanations.

#### Work Step by Step

Step 1. Using the Sum-to- Product Formulas, we have $LHS=\frac{2sin(\frac{2x+6x}{2})cos(\frac{2x-6x}{2})}{2cos(\frac{2x+6x}{2})sin(\frac{2x-6x}{2})}=\frac{sin(4x)cos(2x)}{coos(4x)sin(-2x)}=-\frac{sin(4x)cos(2x)}{coos(4x)sin(2x)}$ Step 2. We have $RHS=-tan(4x)cot(2x)=-\frac{sin(4x)}{cos(4x)}\times\frac{cos(2x)}{sin(2x)}$ Step 3. Since $LHS=RHS$, we verified the identity.

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