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

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.

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.

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.

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

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

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

Latest Math Topics

Jan 06, 2023

Jan 03, 2023

Jan 01, 2023

Dec 26, 2022

Dec 08, 2022

Latest Math Problems

Nov 25, 2022

Nov 02, 2022

Oct 26, 2022

Oct 24, 2022

Sep 30, 2022

A best free mathematics education website for students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Learn how to solve the maths problems in different methods with understandable steps.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved