Hello,

The question I’m working on is

$\displaystyle f(x) = \4cos^2{x} - \3sin^2{x}$

Show that $\displaystyle f(x) = \dfrac{1}{2} +\dfrac{7}{2}\cos2{x} $

I have tried using $\displaystyle \sin^2{x} + \cos^2{x} = 1$

And the double angle identity for $\displaystyle \cos2{x}$

The best I’ve got is

$\displaystyle f(x) = \3cos2{x} + \cos^2{x}$, which it might not be.

Maybe I should be using the half angle identity, but I'm not sure how.

I know I have to work at these, but if someone could point me in the right direction with this I’d be very grateful.

Thank you