# Sections 2.5 Multiple-Angle and Product-to-Sum Formulas

**Section Objectives**

- Use double-angle formulas to rewrite trigonometric expressions.
- Use power-reducing formulas to rewrite trigonometric expressions.
- Use product-to-sum and sum-to-product formulas to rewrite trigonometric equations.

### Double-angle Formulas

The double-angle formulas follow immediately from the sum formulas.

#### Examples

- Find if and is in the 4th quadrant.

- Determine a formula for .

### Power-reducing and Half-angle Formulas

These formulas are easily derived from the double-angle formulas.

#### Examples

- Rewrite in terms of 1st powers of sines and/or cosines.

- Derive a half-angle formula for .

### Product-to-sum formulas

These formulas are easy to derive from the sum and difference formulas.

#### Examples

- Rewrite as a sum or difference.

- Derive a sum-to-product formula and use it to solve .