### Table of Contents

# Integrating cos² x

## Using the Pythagorean identity

Integrate by parts using and :

Add to both sides:

Apply integral linearity:

Apply the Pythagorean identity and divide both sides by 2:

## Using the double angle formula

Careful! This derivation differs from the one in Integrating sin² x by just a sign.

Rewrite the integral using the double angle formula for the cosine:

Substitute :

Substitute back and simplify: