I have tasked with rewriting the following function using Euler's equation into an expression where it is easier to find the indefinite integral
I have no idea where to even begin here. I think I have to make use of the fact that Euler's equation can be rewritten into:
Can anyone give a hint in the right direction here?
Use the fact that $$2\cos(16t)\cos(6t) = \cos(22t)+\cos(10t).$$ Next use Euler's formula to get that $$\cos(22t)+\cos(10t) = \frac{e^{22it}+e^{-22it}}{2}+\frac{e^{10it}+e^{-10it}}{2}.$$
Recall that $$\cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b)$$ and $$\cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b).$$ So $$\cos(a+b)+\cos(a-b)=2\cos(a)\cos(b).$$