Sinx/2+cosx/2=корень из 3

[latex]\sin \dfrac{x}{2}+\cos \dfrac{x}{2}=\sqrt3\\ \sqrt 2 \sin \left(\dfrac{\pi}{4}+x\right)=\sqrt3\\ \sin \left(\dfrac{\pi}{4}+x\right)=\dfrac{\sqrt3}{\sqrt2}\\ \sin \left(\dfrac{\pi}{4}+x\right)=\sqrt{\dfrac{3}{2}}\\ \sqrt{\dfrac{3}{2}}\ \textgreater \ 1 \Rightarrow x \in \emptyset[/latex]