# Multiple angle identities

The trigonometric functions are often appeared with multiple angles. It is not possible to find their values directly but their values can be evaluated by expressing each trigonometric function in its expansion form. Now, learn how to expand trigonometric functions with multiple angles. The following multiple angle identities are used as formulae in mathematics.

### Double angle formulas

Learn how to expand double angle trigonometric functions in terms of trigonometric functions.

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

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

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

$(4)\,\,\,\,$ $\cot{2\theta}$ $\,=\,$ $\dfrac{\cot^2{\theta}-1}{2\cot{\theta}}$

### Triple angle formulas

Learn how to expand triple angle trigonometric functions in terms of trigonometric functions.

$(1)\,\,\,\,$ $\sin{3\theta}$ $\,=\,$ $3\sin{\theta}-4\sin^3{\theta}$

$(2)\,\,\,\,$ $\cos{3\theta}$ $\,=\,$ $4\cos^3{\theta}-3\cos{\theta}$

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

$(4)\,\,\,\,$ $\cot{3\theta}$ $\,=\,$ $\dfrac{3\cot{\theta}-\cot^3{\theta}}{1-3\cot^2{\theta}}$

Latest Math Problems

A best free mathematics education website for students, teachers and researchers.

###### Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

###### Maths Problems

Learn how to solve the maths problems in different methods with understandable steps.

Learn solutions

###### Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.