Math Doubts

Cos double angle identity in terms of Tan

Formula

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

The cos of double angle equals to the quotient of the subtraction of square of tan function from one by the sum of one and square of tan function is called the cos of double angle identity in terms of tan functions.

Introduction

Let theta represents an angle of a right triangle. The cosine of double angle is written as $\cos{2\theta}$ and the square of tangent of angle theta is written as $\tan^2{\theta}$ in mathematical form.

The $\cos{2\theta}$ is equal to the quotient of subtraction of $\tan^2{\theta}$ from $1$ by the addition of $1$ and .$\tan^2{\theta}$.

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

It is called the cos double angle identity in terms of tan function and also used as a formula in trigonometry.

Usage

The cosine of double angle rule is used in two cases in mathematics.

  1. To expand a cos double angle function as the quotient of subtraction of square of tan function from one by the addition of one and square of tan function.
  2. To simplify the quotient of subtraction of square of tan function from one by the sum of one and square of tan function as the cos double angle function.

Popular forms

The cos of double angle rule is written in terms of tan functions popularly in the following two different forms.

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

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

Proof

Learn how to derive the cos double angle formula in terms of tan functions in trigonometric mathematics.

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