Use half angle identities to solve trig equations

Question

Use half angle identities to solve trig equations 

Solve the given equations for the values of x in the interval [0, 2pi]

1) cos^2 x = sin^2 x/2

Answer 1

sin (x/2) = ±√[(1 - cos x) / 2}

sin² (x/2) = (1 - cos x) / 2

cos² x = (1 - cos x) / 2

2 cos² x = 1 - cos x

2 cos² x + cos x - 1 = 0

Can you solve for x and answer?