*This is exactly how the question reads from the book

Using the fact that a complex equation is really two real equations, find the double angle formulas (for Sin2 , Cos2 ) by using this equation: (e^i)^n= (Cos +iSin )^n= Cosn+iSinn

I know if you put in 2 for n and just exapand it out I can get it but I figured that there might be some other way to prove it. Just seems a bit simple but any help or insight would be greatly appriciated.