Help with this math Transformation

[kasse]

Can anyone explain why (cos(x))^2 = (1+cos(2x))/2 ?

 

[ziad1985]

cos(x)=(Exp(ix)+Exp(-ix))/2 right? do u know this formula?
square before and after the '='
then simplify it..

 

[HallsofIvy]

If you don't want to use complex numbers, remember that cos2x= cos² x- sin² x so that the right hand side is (1+ cos² x- sin²x)/2. Do you see an "obvious" way to simplify 1+ cos² x- sin²x?