# Trigonometric multiple and sub-multiple angle formulas

**Trigonometric multiple and sub-multiple angle formulas**:

*Prerequisite*: Please consider studying following topics before you study this article for better grasp and understanding:

Trigonometric addition and subtraction formulas

In this tutorial we shall derive formula for trigonometric functions of multiple and sub-multiple angle , For example:

etc.

**Trigonometric multiple angle formulas**:

Under the trigonometric multiple angle formulas we shall derive the formulas for double and triple and trigonometric formulas which are listed below:

**Double Angle Formulas**:

If In the trigonometric Addition and subtraction formulae we put angle A=B then we can easily derive following double angle formulas:

From the cosine double angle formula above ; we can also derive:

**Triple Angle Formulas**:

We shall now Derive the formulas for triple angle formulas for Sine and Cosine.

We know ,

And :

**Trigonometric Sub-Multiple angle formulas**:

We shall now derive the trigonometric formulas for half angle formulas.

**Half angle formulas**:

By replacing by In the double angle formulas above we can easily derive the following half angle formulas:

Related posts:

- Trigonometric functions of negative angles Trigonometric functions of negative angles. How to find trigonometric functions...
- Integration by trigonometric substitution integration by trigonometric substitution: One of the most powerful techniques...
- Derivatives of inverse trigonometric functions Inverse trigonometric functions are the inverse of trigonometric functions ....
- Pythagorian Identities Fundamental Pythagorian identity of trigonometry and other basic trigonometric formulas...
- Trigonometric Addition and Subtraction formulae Trigonometric Addition and Subtraction formulae. Angle addition Addition and subtraction...