Factor each expression:
cos^2x- 2cosx+1
4cos^2x-1
call z = cos x
z^2 -2z +1
(z-1)(z-1)
so
(cosx-1)(cosx+1)
4z^2-1
(2z-1)(2z+1)
(2cosx-1)(2cosx+1)
cos^2x- 2cosx+1
4cos^2x-1
z^2 -2z +1
(z-1)(z-1)
so
(cosx-1)(cosx+1)
4z^2-1
(2z-1)(2z+1)
(2cosx-1)(2cosx+1)