Use trig identity:
sin 2x = 2sin x.cos x.
In this case:
sin^2 x = 4sin^2 (x/2).cos^2 (x/2)
Rewrite the equation:
4sin^2 (x/2).cos^2 (x/2) - cos^2 (x/2) = 0
cos^2 (x/2)(4sin^2 (x/2) - 1) = 0
Either factor must be zero.
a. cos^2 (x/2) = 0 --> cos (x/2) = 0
Unit circle gives 2 solutions:
x/2 = pi/2 + 2kpi --> x = pi + 4kpi, and
x/2 = (3pi)/2 + 2kpi--> x = 3pi + 4kpi
b. 4sin^2 (x/2) = 1 --> sin^2 (x/2) = 1/4
sin (x/2) = +- 1/2
Trig table and unit circle give 2 solutions:
a. sin x = 1/2 --> x/2 = pi/6 + 2kpi --> x = pi/3 + 4kpi
and x/2 = (5pi)6 + 2kpi --> x = (5pi)/3 + 4kpi
b. sin x = - 1/2 --> x/2 = (7pi)/6 + 2kpi -->
x = (7pi)/3 = (pi/3) + 4kpi , and
x/2 = (11pi)/6 + 2kpi --> x = (11pi)/3 = (5pi)/3 + 4kpi
