The cosine double angle identity can be expanded in terms of square of sine function as follows.

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

Now, it is your turn to learn how to prove the cos double angle identity in terms of sine squared function in trigonometry.

In mathematics, the sine in square form is written as $\sin^2{\theta}$ and cosine of double angle function is written as $\cos{2\theta}$ when the angle of a right triangle is denoted by theta.

According to the cos double identity proof, the cosine of double angle is equal to the difference of the squares of sine and cosine of angle.

$\cos{2\theta}$ $\,=\,$ $\cos^2{\theta}-\sin^2{\theta}$

According to the cosine squared identity, the square of cos function can be written in terms of square of sin function.

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

Now, simplify the right hand side trigonometric expression of the equation for deriving the expansion of cos double angle formula in square of sine function.

$\implies$ $\cos{2\theta}$ $\,=\,$ $1-\sin^2{\theta}-\sin^2{\theta}$

$\,\,\,\therefore\,\,\,\,\,\,$ $\cos{2\theta}$ $\,=\,$ $1-2\sin^2{\theta}$

The angle in this cosine double angle identity can be represented by any symbol. However, it is popularly written in the following two forms. You can derive this trigonometric identity in terms of any symbol by the above steps.

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

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

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