# Cosine squared Power reduction identities

## Formulae

$(1).\,\,\,$ $\cos^2{\theta} \,=\, \dfrac{1+\cos{(2\theta)}}{2}$

$(2).\,\,\,$ $\cos^2{\Bigg(\dfrac{\theta}{2}\Bigg)} \,=\, \dfrac{1+\cos{\theta}}{2}$

A trigonometric identity that expresses the reduction of square of cosine function in terms of cosine is called the power reduction identity of cosine squared function.

### Introduction

There are two popular cosine squared power reducing trigonometric identities in mathematics and they are used as formulas in trigonometry.

When the theta represents an angle of a right triangle, the double angle and half angles are written as $2\theta$ and $\dfrac{\theta}{2}$ respectively. The cosine of angle and the square of cosine of angle are written in mathematical form as $\cos{\theta}$ and $\cos^2{\theta}$ respectively. The cosine of double angle is written as $\cos{2\theta}$ and the cosine squared of half angle is written as $\cos^2{\Big(\dfrac{\theta}{2}\Big)}$ mathematically.

Now, the power reducing identities in terms of the cosine squared functions are written mathematically in trigonometric mathematics in the following two forms.

#### Angle to Double angle form

$\cos^2{\theta} \,=\, \dfrac{1+\cos{(2\theta)}}{2}$

The cosine squared of angle is equal to the quotient of one plus cos of double angle by two.

#### Half angle to Angle form

$\cos^2{\Bigg(\dfrac{\theta}{2}\Bigg)} \,=\, \dfrac{1+\cos{\theta}}{2}$

The cosine squared of half angle is equal to the quotient of one plus cosine of angle by two.

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