Chapter 6 - Analytic Trigonometry - Section 6.7 Product-to-Sum and Sum-to-Product Formulas - 6.7 Assess Your Understanding - Page 524: 34

See below.

Use the Sum-to-Product Formula, we have: $LHS=\frac{sin(4\theta)-sin(8\theta)}{cos(4\theta)-cos(8\theta)}=\frac{2cos(\frac{4\theta+8\theta}{2})sin(\frac{4\theta-8\theta}{2})}{-2sin(\frac{4\theta+8\theta}{2})sin(\frac{4\theta-8\theta}{2})} =-\frac{cos(6\theta)}{sin(6\theta)}=-cot(6\theta)=RHS$