Answer
$\frac{\pi}{4},\frac{3\pi}{4},\frac{5 \pi}{4}\frac{7 \pi}{4}$
Work Step by Step
We need to find the range for $x$ for the equation
$2sin^{2}x=1$
$sin^{2}x=\frac{1}{2}$
or
$sinx=±\frac{1}{\sqrt 2} =±\frac{\sqrt 2}{ 2}$
This is true for x=$\frac{\pi}{4},\frac{3\pi}{4},\frac{5 \pi}{4}\frac{7 \pi}{4}$