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

The square of cosine function equals to the subtraction of square of sin function from one is called the cosine squared formula. It is also called as the square of cos function identity.

In trigonometric expressions and equations, the cosine functions are often involved in square form. The equations or expressions can be simplified only by transforming the square of cosine functions into its equivalent form. Therefore, it is very important to learn the square of cosine function formula for studying the trigonometry further.

The cosine squared trigonometric identity is mainly used as a formula in two cases.

- The square of cos function is expanded as the subtraction of sin squared function from one.
- The subtraction of sin squared function from one is simplified as the square of cos function.

The cosine squared function rule is also expressed popularly in two forms in mathematics.

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

Thus, you can express the square of cosine function formula in terms of any angle in trigonometry.

Let’s assume, theta is an angle of a right triangle, then the cosine and sine are written mathematically as $\cos{\theta}$ and $\sin{\theta}$ respectively. As per the Pythagorean identity of sin and cos functions, the mathematical relationship between cosine and sine can be written in the following mathematical form.

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

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

So, it is proved that the square of cosine function is equal to the subtraction of the square of sine function from one.

Latest Math Topics

Jul 24, 2022

Jul 15, 2022

Jun 01, 2022

Latest Math Problems

Jul 29, 2022

Jul 17, 2022

Jun 02, 2022

Apr 06, 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