### Home > PC > Chapter 5 > Lesson 5.2.4 > Problem5-90

5-90.

Verify the following trigonometric identities. Intermediate steps may involve complex fractions.

1. $\csc^{2} x + \sec^{2} x − \tan^{2} x −\cot^{2} x = 2$

Fundamental Pythagorean Identities:
$\sin^{2}θ + \cos^{2}θ = 1$
$1 + \tan^{2}θ = \sec^{2}θ$
$1 + \cot^{2}θ = \csc^{2}θ$

2. $\frac { \operatorname { sec } x - 1 } { 1 - \operatorname { cos } x } = \operatorname { sec } x$

Change all terms to sine and cosine.