Question

How do you use a double angle identity to find the exact value of each expression?

Answer 1

You would need an expression to work with.

For example:
Given `sinalpha=3/5` and `cosalpha=-4/5`, you could find `sin2 alpha` by using the double angle identity
`sin2 alpha=2sin alpha cos alpha`.

`sin2 alpha=2(3/5)(-4/5)=-24/25`.

You could find `cos2 alpha` by using any of:
`cos2 alpha=cos^2 alpha -sin^2 alpha`
`cos2 alpha=1 -2sin^2 alpha`
`cos2 alpha=2cos^2 alpha -1`

In any case, you get `cos alpha=7/25`.