Help solving trigonometric equation?

Question

here is the equation : 2sin^2x = 1

I got sin^2x = 1/2

then ... what's next ?

Answer 1

2 sin^2(x) = 1

1 - 2 sin^2(x) = 0

cos(2x) = 0

2x = pi / 2 + 2n pi or 3pi / 2 + 2n pi where n is any integer,

x = pi / 4 + n pi or 3pi / 4 + n pi.

Using your method:

sin^2(x) = 1 / 2

sin(x) = +/- 1 / sqrt(2)

x = pi / 4 + 2n pi, 3pi / 4 + 2n pi, 5pi / 4 + 2n pi, 7pi / 4 + 2n pi

= pi / 4 + n pi or 3pi / 4 + n pi.