Chapter 6 - Analytic Trigonometry - Section 6.6 Double-angle and Half-angle Formulas - 6.6 Assess Your Understanding - Page 519: 63

See below.

$LHS=\frac{sin(3\theta)}{sin\theta}-\frac{cos(3\theta)}{cos\theta} =\frac{sin(\theta+2\theta)}{sin\theta}-\frac{cos(\theta+2\theta)}{cos\theta} =\frac{sin(\theta)cos(2\theta)+cos(\theta)sin(2\theta)}{sin\theta}-\frac{cos(\theta)cos(2\theta)-sin(\theta)sin(2\theta)}{cos\theta} =cos(2\theta)+2cos^2\theta-cos(2\theta)+2sin^2\theta=2=RHS$