$\tan{2\theta} \,=\, \dfrac{2\tan{\theta}}{1-\tan^2{\theta}}$

$\dfrac{2\tan{\theta}}{1-\tan^2{\theta}} \,=\, \tan{2\theta}$

It is called tan double angle identity and used as a formula in two cases.

- Tan of double angle is expanded as the quotient of twice the tan function by subtraction of square of tan function from one.
- The quotient of twice the tan function by subtraction of square of tan function from one is simplified as tan of double angle.

The tangent of double angle identity is used to either expand or simplify the double angle functions like $\tan{2A}$, $\tan{2x}$, $\tan{2\alpha}$ and etc. For example,

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

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

$(3) \,\,\,\,\,\,$ $\tan{2\alpha} \,=\, \dfrac{2\tan{\alpha}}{1-\tan^2{\alpha}}$

Learn how to derive the rule of tan double angle identity by geometric approach in trigonometry.

List of most recently solved mathematics problems.

Jul 04, 2018

Limit (Calculus)

Evaluate $\displaystyle \large \lim_{x \,\to\, \tan^{-1}{3}} \normalsize {\dfrac{\tan^2{x}-2\tan{x}-3}{\tan^2{x}-4\tan{x}+3}}$

Jun 23, 2018

Limit (Calculus)

Evaluate $\displaystyle \large \lim_{x \to 0} \normalsize \dfrac{e^{x^2}-\cos{x}}{x^2}$

Jun 22, 2018

Integral Calculus

Evaluate $\displaystyle \int \dfrac{1+\cos{4x}}{\cot{x}-\tan{x}} dx$

Jun 21, 2018

Limit

Evaluate $\displaystyle \large \lim_{x \to \infty} \normalsize {\sqrt{x^2+x+1}-\sqrt{x^2+1}}$

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.