I have the following expression which I've been told to simplify using Eulers equation:
$$\cos(22t)+\cos(10t)$$
I think I have to substitute these expressions in (from rewriting Eulers equation)
$$\cos(22t)+\cos(10t)=\frac{e^{i22t}+e^{-i22t}}2+\frac{e^{i10t}+e^{-i10t}}2$$
But I just have no idea where to go from here. Can anyone give me a hint?
As pointed out in the comments, this expression is equal to: $$\dfrac { \left( e ^ { 16 i t } + e ^ { - 16 i t } \right) \left( e ^ { 6 i t } + e ^ { - 6 i t } \right) } { 2 }$$
Using Euler's formula again, we get: $$\cos(22t) + \cos(10t) =\dfrac { 2\cos(16t) \cdot 2 \cos(6t) } { 2 } = 2\cos(16t) \cos(6t).$$