Chapter 7 - Analytic Trigonometry - 7.6 Double-angle and Half-angle Formulas - 7.6 Assess Your Understanding - Page 498: 66

See below.

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