Stud the sign of :
$\displaystyle cos(x)+ \sqrt{3} sin(x)= 0$ when $\displaystyle tan(x)= \frac{sin(x)}{cos(x)}= \frac{1}{\sqrt{3}$ and that happens when $\displaystyle x= \pi/6+ k\pi$. $\displaystyle sin^2(x)- 1/2= 0$ when $\displaystyle sin(x)= \pm\frac{1}{\sqrt{2}}$ and that happens when $\displaystyle x= k\pi/4$. Those points are the only places you expression can change sign.