do you realize that $\displaystyle \sin^2 x$ is always non-negative? it's a square term, so it is greater than or equal to zero (it is also less than or equal to 1, to be precise)
$\displaystyle 2 \sin^2 x + 1 = 0$
means $\displaystyle 2 \sin^2 x = -1$
but -1 is negative, thus we cannot solve this for any real number x
got it?