Verify cosxcosy = 1/2 [cos(x+y) + cos(x-y)]
I think the inner part is goofing me up.
I never get far . Please help.
$\displaystyle \displaystyle \begin{align*}\frac{1}{2}\left[\cos{(x + y)} + \cos{(x - y)}\right] &\equiv \frac{1}{2}\left[\cos{(x)}\cos{(y)} - \sin{(x)}\sin{(y)} + \cos{(x)}\cos{(y)} + \sin{(x)}\sin{(y)}\right] \\ &\equiv \frac{1}{2}\left[2\cos{(x)}\cos{(y)}\right] \\ &\equiv \cos{(x)}\cos{(y)} \end{align*}$