Math Doubts

Addition of 1 and Cos double angle formula

Formula

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

The sum of one and cosine of double angle function equals to two times the square of cosine of angle is called the addition of one and cos double angle identity.

Introduction

Let theta ($\theta$) represents an angle of a right triangle, the cos of double angle function is written as $\cos{2\theta}$ in trigonometry and the addition of one and cosine of double angle function is written as $1+\cos{2\theta}$ in mathematics.

The trigonometric expression $1+\cos{2\theta}$ can be simplified as two times the cos squared of angle and it is written as $2\cos^2{\theta}$.

Popular forms

The sum of one and cosine of double angle identity is written in two different forms popularly.

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

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

Usage

A trigonometric expression that is in the form of sum of one and cosine of double angle function, is simplified as the two times the cosine squared of angle.

Proof

Learn how to derive the sum one and cosine of double angle identity in trigonometry.

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