Chapter 6 - Analytic Trigonometry - Section 6.4 Trigonometric Identities - 6.4 Assess Your Understanding - Page 497: 77

See below.

$LHS=\frac{sec\theta}{1-sin\theta}=\frac{sec\theta}{1-sin\theta}\times\frac{1+sin\theta}{1+sin\theta}=\frac{sec\theta+sec\theta sin\theta}{1-sin^2\theta}=\frac{sec\theta+sec\theta sin\theta}{cos^2\theta}\times\frac{cos\theta}{cos\theta}=\frac{1+sin\theta}{cos^3\theta}=RHS$