Question

How do you use the double angle formula to rewrite `5-10sin^2x`?

Answer 1

Think about (list) double angle formulas until you come to one that looks useful.

`sin(2 theta) = 2sin theta cos theta` Doesn't look helpful

`cos(2 theta) = cos^2 theta - sin^2 theta` -- Hmmmm, probably not but there are other forms for this one

`cos(2 theta) = 1 - 2sin^2 theta`. Compare this to what we started with.

If I factored out a 5, I'd have:

`5-10sin^2x = 5(1-2sin^2x)` and that's just

`5cos(2x)`

So there it is.

`5-10sin^2x = 5cos(2x)`