Cos2x+0.5/cosx/sinx=0

[latex] \frac{cos2x+0,5}{ \frac{cosx}{sinx}}=0 \\ \frac{sinx(cos2x+0,5)}{cosx}=0 \\ \frac{sinxcos2x+0,5sinx}{cosx}=0 \\ \frac{sinx(cos^{2}x-sin^{2}x)+0,5sinx}{cosx}=0 \\ \frac{sinxcos^{2}x-sin^{3}x+0,5sinx}{cosx}=0 \\ \frac{sinx(1-sin^{2}x)-sin^{3}x+0,5sinx}{cosx}=0 \\ \frac{sinx-sin^{3}x-sin^{3}x+0,5sinx}{cosx}=0 \\ \frac{-2sin^{3}x+1,5sinx}{cosx}=0 \\ \frac{sinx(-2sin^{2}x+1,5)}{cosx}=0|*cosx \\ \\ sinx(-2sin^{2}x+1,5)=0 \\ -2sin^{2}x+1,5=0 \\ -2sin^{2}x=-1,5|*(-1) \\ 2sin^{2}x=1,5 \\ sin^{2}x=0,75[/latex][latex]0,75= \frac{3}{4} \\ sin^{2}x= \frac{3}{4} \\ sinx= \sqrt{ \frac{3}{4}} \\ sinx= \frac{ \sqrt{3}}{2} \\ x=(-1)^{n} \frac{ \pi }{3}+ \pi n[/latex]