Fundamentals and Basic Identities

Whenever you see a trigonometric function squared, start looking for a Pythagorean identity.

The two identities used in this problem are ${\displaystyle {\sin }^2<!--\; \; -->x+{\cos }^2<!--\; \; -->x=1}$ and ${\displaystyle {\tan }^2<!--\; \; -->x+1={\sec }^2<!--\; \; -->x}$

Substitute and solve.

${\displaystyle {\sin }^2<!--\; \; -->x+{\cos }^2<!--\; \; -->x+{\tan }^2<!--\; \; -->x=?}$

${\displaystyle ({\sin }^2<!--\; \; -->x+{\cos }^2<!--\; \; -->x)+{\tan }^2<!--\; \; -->x=?}$

${\displaystyle (1)+{\tan }^2<!--\; \; -->x={\sec }^2<!--\; \; -->x}$