![image](https://tex.z-dn.net/?f=%5Ccos+x%3D%5Cfrac12%3B%5C%5C%0A%5Csin2x-%3F%3B%5C%5C%0A%5Csin2x%3D2%5Ccdot%5Csin+x%5Ccdot%5Ccos+x%3B%5C%5C%0A%5Csin%5E2x%2B%5Ccos%5E2x%3D1%3B%3D%3D%3E%5Csin%5E2x%3D1-%5Ccos%5E2x%3B%5C%5C%0A%5Csin2%3D%5Cpm%5Csqrt%7B1-%5Ccos%5E2x%7D%3D%5Cpm%5Csqrt%7B1-%5Cleft%28%5Cfrac12%5Cright%29%5E2%7D%3D%5Cpm%5Csqrt%7B1-%5Cfrac14%7D%3D%5C%5C%0A%3D%5Cpm%5Csqrt%7B%5Cfrac44-%5Cfrac14%7D%3D%5Cpm%5Csqrt%7B%5Cfrac%7B4-1%7D%7B4%7D%7D%3D%5Cpm%5Csqrt%7B%5Cfrac34%7D%3D%5Cpm%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%3B%5C%5C%0A%5Csin2x%3D2%5Ccdot%5Cleft%28%5Cpm%5Cfrac%7B%5Csqrt3%7D%7B2%7D%5Cright%29%5Ccdot%5Cfrac12%3D%5Cpm%5Cfrac%7B%5Csqrt3%7D%7B2%7D.)
\sin^2x=1-\cos^2x;\\
\sin2=\pm\sqrt{1-\cos^2x}=\pm\sqrt{1-\left(\frac12\right)^2}=\pm\sqrt{1-\frac14}=\\
=\pm\sqrt{\frac44-\frac14}=\pm\sqrt{\frac{4-1}{4}}=\pm\sqrt{\frac34}=\pm\frac{\sqrt{3}}{2};\\
\sin2x=2\cdot\left(\pm\frac{\sqrt3}{2}\right)\cdot\frac12=\pm\frac{\sqrt3}{2}." alt="\cos x=\frac12;\\
\sin2x-?;\\
\sin2x=2\cdot\sin x\cdot\cos x;\\
\sin^2x+\cos^2x=1;==>\sin^2x=1-\cos^2x;\\
\sin2=\pm\sqrt{1-\cos^2x}=\pm\sqrt{1-\left(\frac12\right)^2}=\pm\sqrt{1-\frac14}=\\
=\pm\sqrt{\frac44-\frac14}=\pm\sqrt{\frac{4-1}{4}}=\pm\sqrt{\frac34}=\pm\frac{\sqrt{3}}{2};\\
\sin2x=2\cdot\left(\pm\frac{\sqrt3}{2}\right)\cdot\frac12=\pm\frac{\sqrt3}{2}." align="absmiddle" class="latex-formula">