# Double Angle Formula – Explanation and Examples

The double angle formula gives the trigonometric ratio for an angle twice a given angle.

There are double angle formulas for sine and cosine. The formulas for the other trig functions follow from these.

Since the double angle formula gives exact values for trig ratios of minor angles, it is useful for ensuring accuracy in engineering, astronomy, and other physical sciences.

This section covers:

• What is the Double Angle Formula?
• Proof of the Double Angle Formula
• Cos Double Angle Formula
• Sin Double Angle Formula
• Tangent Double Angle Formula

## What is the Double Angle Formula?

The double angle formula is an equation that gives the trigonometric ratio for an angle equal to twice a given angle.

For a trigonometric function $f(x)$, $f(2x) \neq f(x)$. This means that doubling the trig ratio for an angle is not the same as finding the trig ratio for twice the angle.

Instead, the double angle for $sin(2x)$ is:

$2sinxcosx$.

For cosine, the double angle formula is:

$cos^2x-sin^2x$.

Alternatively, the double angle formula for cosine is written as:

$1-2sin^2x$ or $2cos^2x-1$.

### Proof of the Double Angle Formula

The proofs for the double angle formulas come from the sum formulas.