# Cos Double angle formula

## Formula

$\cos{(2\theta)} \,=\, \cos^2{\theta}-\sin^2{\theta}$

The cos of double angle is equal to the subtraction of square of sin of angle from square of cos of angle. It is called the cos of double angle identity and used as a formula in trigonometry.

### Introduction

Theta is an angle of right triangle. Then the cosine of double angle is written as $\cos{2\theta}$ and the squares of sine and cosine of angle are written in mathematical form as $\sin^2{\theta}$ and $\cos^2{\theta}$ respectively.

The $\cos{2\theta}$ is equal to the subtraction of the sine squared theta from cos squared theta.

$\cos{(2\theta)} \,=\, \cos^2{\theta}-\sin^2{\theta}$

It is called the cos double angle identity and used as a formula in mathematics.

#### Usage

The cosine of double angle identity is used in different ways in mathematics.

1. It is used to expand the cos double angle function as the subtraction of square of sin function from the square of cosine function.
2. It is also used to simplify the difference of square of sine function from square of cosine function as the cos double angle function.

### Popular forms

The cos double angle formula is written in terms of any angle and the following three are the popular forms of double angle identity of cosine function.

$(1) \,\,\,$ $\cos{2x} \,\,=\, \cos^2{x}-\sin^2{x}$

$(2) \,\,\,$ $\cos{2A} \,=\, \cos^2{A}-\sin^2{A}$

$(3) \,\,\,$ $\cos{2\theta} \,\,=\, \cos^2{\theta}-\sin^2{\theta}$

#### Proof

Learn how to derive the rule for cos double angle identity in mathematical form.

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