Chapter 1 - Functions - 1.4 Trigonometric Functions and Their Inverse - 1.4 Exercises - Page 48: 31

$\textbf{See Step By Step for Proof.}$

$tan^2(\theta) + 1 = sec^2(\theta)$ $\frac{sin^2(\theta)}{cos^2(\theta)}+1 = sec^2(\theta)$ $\frac{sin^2(\theta)+cos^2(\theta)}{cos^2(\theta)} = sec^2(\theta)$ $\dfrac{1}{cos^2(\theta)} = sec^2(\theta)$ $sec^2(\theta) = sec^2(\theta)$