Math Doubts

Cosine squared Power reduction identity


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

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


The cosine of angles are appeared in square form in trigonometric mathematics. In some special cases, it is essential to transform the square of cosine function into other form. In fact, it is possible for reducing the square of cosine of angle by writing it in terms of cosine of double angle. It is called the power reducing trigonometric identity for cosine squared of angle.

When the angle of a right triangle (right angled triangle) is denoted by the symbol theta, the cosine squared of angle is written as $\cos^2{\theta}$ and cosine of double angle is written as $\cos{2\theta}$ in mathematical form.

The square of cosine of angle is equal to the quotient of one plus cosine of double angle by two. it can be expressed in mathematical form as follows.

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

The mathematical equation is called the power reducing identity of cosine squared of angle.

Other forms

The angle in this power reducing trigonometric formula can be denoted by any symbol and it is popularly written in the following two forms.

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

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

In this way, you can write the cosine squared power reducing trigonometric identity in terms of any symbol.


Learn how to prove the cosine squared power reduction trigonometric identity in trigonometry.

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