Question

I need some help figuring out how to prove `cos^2x = (1+cos(2x))/2` ? (the x isn’t part of the exponent but I’m not sure how to signal that when typing) Thanks!

Answer 1

`LHS= cos^2x`

`= 1/2*(2cos^2x)`

`= 1/2*(cos^2x+1-sin^2x)`

`= 1/2*(1+(cosx*cosx-sinx*sinx))`

`= (1+cos(x+x))/2`

`= (1+cos(2x))/2=RHS`