Double Angle Formulæ

MathsDirect

Double angle formulæ are alternative ways of writing sin2x, cos2x, etc. They are useful for integration, and arise from the compound angle formulæ.

Remember the formulæ

These can be adapted to double fomulæ by replacing the B with another A

These are the three double angle formulæ

Notice that there are 3 forms of the cos formula.

To see where these could be useful, consider the following,

We do not know how to perform this integration, but the double angle formula suggests a way

There is now nothing in the expression that we cannot integrate

The idea of double angle formulæ can be extended, using the compound angle formulæ