# Cosine double angle identity in square of Cosine

## Formula

$\cos{2\theta}$ $\,=\,$ $2\cos^2{\theta}-1$

A mathematical identity that expresses the expansion of cosine of double angle in terms of cosine squared of angle is called the cosine of double angle identity in square of cosine.

### Introduction

When the theta represents an angle of a right triangle, the cosine of double angle and cosine squared of angle are written as $\cos{2\theta}$ and $\cos^2{\theta}$ respectively.

The cosine of double angle is equal to the subtraction of one from two times the square of cosine.

$\cos{2\theta}$ $\,=\,$ $2\cos^2{\theta}-1$

It is called the cosine of double angle identity in terms of cosine squared form.

#### Usage

In trigonometry, it can be used as a formula in two distinct cases.

##### Expansion

It is used to expand the cosine of double angle functions as the subtraction of one from two times the cosine squared of angle.

$\implies$ $\cos{2\theta}$ $\,=\,$ $2\cos^2{\theta}-1$

##### Simplified form

It is also used to simplify the subtraction of one from two times the cosine squared of angle as the cosine of double angle function.

$\implies$ $2\cos^2{\theta}-1$ $\,=\,$ $\cos{2\theta}$

#### Other forms

The angle in cos of double angle formula can be represented by any symbol. Therefore, it is popularly written in two other forms.

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

$(2). \,\,\,\,\,\,$ $\cos{2A}$ $\,=\,$ $2\cos^2{A}-1$

#### Proof

Learn how to derive the rule for the cosine of double angle in terms of square of cosine function in trigonometry.

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