Math Doubts

Subtraction of Cos double angle from one formula

Formula

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

The subtraction of cosine of double angle function from one is equal to two times the square of sine of angle. It is called the subtraction of cos double angle from one identity.

Introduction

Let theta ($\theta$) be an angle of a right triangle, the cosine of double angle is written as $\cos{2\theta}$ mathematically and the subtraction of cosine of double angle function from one is written as $1-\cos{2\theta}$ in trigonometric mathematics.

The trigonometric expression $1-\cos{2\theta}$ can be simplified and it is equal to two times the square of sine of angle, which means $2\sin^2{\theta}$.

Popular forms

The subtraction of cosine of double angle function from one identity is popularly written in two forms.

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

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

Usage

A trigonometric expression that is in the form of subtracting cosine of double angle function from one, is simplified as the sine squared of angle.

Proof

Learn how to derive an identity for the subtraction of cosine of double angle function from one.

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