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Sine squared Power reduction identity

Formula

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

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

Introduction

The sine functions are appeared in square form in mathematics. In some cases, it is essential to convert the square of sine function into other form. Actually, it is possible to reduce the square of sine of angle by expressing it in terms of cosine of double angle and it is called the power reducing trigonometric identity of sine squared of angle.

Let theta denotes the angle of a right triangle (right angled triangle). The sine squared of angle is written as $\sin^2{\theta}$ and cosine of double angle is written as $\cos{2\theta}$ in mathematical form.

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

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

This mathematical equation is called the power reducing trigonometric identity of sine squared of angle.

Other forms

The angle in this trigonometric formula can be denoted by any symbol. The following two are the some popular forms for the power reducing identity of sine squared of angle function.

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

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

Proof

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

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