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

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

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

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

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

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

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

The sine squared of angle is equal to the quotient of one minus cos of double angle by two.

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

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

Latest Math Topics

Apr 18, 2022

Apr 14, 2022

Apr 05, 2022

Mar 18, 2022

Mar 05, 2022

Latest Math Problems

Apr 06, 2022

Mar 22, 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 - 2021 Math Doubts, All Rights Reserved