Chapter 7 - Analytic Trigonometry - 7.6 Double-angle and Half-angle Formulas - 7.6 Assess Your Understanding - Page 498: 50

See below.

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