prove that

Question

(2cosx+1)(2cosx-1)= 1 +2cos2x

Answer 1

Using
cos(2x)=cos²(x)-sin²(x)
and cos²(x)=1-sin²(x)
expand the right-hand-side to
4cos²(x)-1
which easily factorizes to the left-hand-side, namely:
(2cosx+1)(2cosx-1)

Answer 2

How did you find 4cos^2-1 when expanding the right side