Math Doubts

Sin squared formula


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

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


The sine functions are often appeared in square form in trigonometric expressions and equations. They can be simplified by transforming the square of sine functions into its equivalent form. So, it is essential to learn the square of sine function identity for studying the trigonometry further.


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

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

Popular forms

The square of sine function rule is also expressed in two popular forms in mathematics.

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

In this way, you can write the square of sine function rule in terms of any angle in mathematics.


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

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

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

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

Math Questions

The math problems with solutions to learn how to solve a problem.

Learn solutions

Math Worksheets

The math worksheets with answers for your practice with examples.

Practice now

Math Videos

The math videos tutorials with visual graphics to learn every concept.

Watch now

Subscribe us

Get the latest math updates from the Math Doubts by subscribing us.

Learn more

Math Doubts

A free math education service for students to learn every math concept easily, for teachers to teach mathematics understandably and for mathematicians to share their maths researching projects.

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved