Chapter 6 - Analytic Trigonometry - Section 6.6 Double-angle and Half-angle Formulas - 6.6 Assess Your Understanding - Page 519: 64

See below.

$LHS=\frac{cos\theta+sin\theta}{cos\theta-sin\theta}-\frac{cos\theta-sin\theta}{cos\theta+sin\theta} =\frac{(cos\theta+sin\theta)^2-(cos\theta-sin\theta)^2}{(cos\theta-sin\theta)(cos\theta+sin\theta)} =\frac{4sin\theta cos\theta}{cos^2\theta-sin^2\theta} =\frac{2sin(2\theta)}{cos(2\theta)} =2tan(2\theta)=RHS$