√3-2√3sinx11П/12
c пояснением плес

[tex]\sqrt3-2\sqrt3sin\frac{11\pi}{12}=\sqrt3-2\sqrt3sin(\pi -\frac{\pi}{12})=\sqrt3-2\sqrt3sin\frac{\pi}{12}=\\\\=\sqrt3-2\sqrt3\cdot \frac{\sqrt3-1}{2\sqrt2} =\sqrt3- \frac{\sqrt3(\sqrt3-1)}{\sqrt2} =\sqrt3- \frac{\sqrt6(\sqrt3-1)}{2} =\\\\= \frac{2\sqrt3-3\sqrt2+\sqrt6}{2}[/tex]

[tex]P.S.\; \; sin\frac{\pi}{12}=sin15^\circ=sin(45^\circ -sin30^\circ )=\\\\=sin45\cdot cos30-sin30\cdot cos45= \frac{\sqrt2}{2} \cdot \frac{\sqrt3}{2} - \frac{1}{2} \cdot \frac{\sqrt2}{2}=\\\\= \frac{\sqrt2}{2}\cdot \frac{\sqrt3-1}{2}=\frac{\sqrt3-1}{2\sqrt2} [/tex]