verify the identity

Question

2sin^2(x/2)+4cos^2(x/2)-3=cos(x)

Answer 1

2sin^2(x/2)+4cos^2(x/2)-3
= 2sin^2(x/2)+2cos^2(x/2) + 2cos^2(x/2)-3
= 2 + 2cos^2(x/2) - 3
= 2cos^2(x/2) - 1
= cos(x)