Math Doubts

Cos Double angle formula

Formula

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

The cos of double angle equals to the subtraction of square of sin of angle from square of cos of angle is called the cos of double angle identity.

Introduction

Theta is an angle of right triangle. Then the cosine of double angle is written as $\cos{2\theta}$ and the squares of sine and cosine of angle are written in mathematical form as $\sin^2{\theta}$ and $\cos^2{\theta}$ respectively.

The $\cos{2\theta}$ is equal to the subtraction of the sine squared theta from cos squared theta.

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

It is called the cos double angle identity and used as a formula in mathematics.

Usage

The cosine of double angle identity is used in two different cases in trigonometry.

  1. To expand a cos double angle function as the subtraction of square of sin function from the square of cosine function.
  2. To simplify the difference of square of sine function from square of cosine function as the cos double angle function.

Popular forms

The cos of double angle formula is popularly written in the following two mathematical forms.

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

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

Proof

Learn how to derive the cos double angle rule in mathematical form by geometrical approach.

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