Question

How do you use the double angle or half angle formulas to simplify `6cos^2 x - 3`?

Answer 1

The identity `cos^2x = (1 + cos(2x))/2` would be of use.

`=> 6*(1 + cos(2x))/2 - 3`

`= 3*(1 + cos(2x)) - 3`

`= cancel(3) + 3cos(2x) - cancel(3)`

`= color(blue)(3cos(2x))`

Now, you could use `cos(2x) = cos^2x - sin^2x`, but you would be going backwards in putting back `cos^2x`. Therefore, you would be done here.