1. ## Adding trig functions

Hello,

Can someone please tell me how to add trig functions?

for example, what do you add cos2x? is it cosx+cosx = cos2x?

2. Using the identity

$\cos(a + b) = \cos a \cos b - \sin a \sin b$,

we have

$\cos(2x) = \cos(x + x) = \cos^2x - \sin^2x$.

Then, using the identity

$\sin^2x + \cos^2x = 1$

we have

$\cos(2x) = 2 \cos^2x - 1 = 1 - 2\sin^2x$