Chapter 6 - Analytic Trigonometry - Section 6.6 Double-angle and Half-angle Formulas - 6.6 Assess Your Understanding - Page 519: 48

See below.

$LHS=\frac{cot\theta-tan\theta}{cot\theta+tan\theta} =\frac{cot\theta-tan\theta}{cot\theta+tan\theta}\times\frac{sin\theta cos\theta}{sin\theta cos\theta} =\frac{cos^2\theta-sin^2\theta}{cos^2\theta+sin^2\theta} =\frac{cos(2\theta)}{1}=cos(2\theta)=RHS$