Question

√3-2√3sinx11П/12
c пояснением плес

Answer 1

$sqrt3-2sqrt3sinfrac{11pi}{12}=sqrt3-2sqrt3sin(pi -frac{pi}{12})=sqrt3-2sqrt3sinfrac{pi}{12}=\\=sqrt3-2sqrt3cdot frac{sqrt3-1}{2sqrt2} =sqrt3- frac{sqrt3(sqrt3-1)}{sqrt2} =sqrt3- frac{sqrt6(sqrt3-1)}{2} =\\= frac{2sqrt3-3sqrt2+sqrt6}{2}$

$P.S.; ; sinfrac{pi}{12}=sin15^circ=sin(45^circ -sin30^circ )=\\=sin45cdot cos30-sin30cdot cos45= frac{sqrt2}{2} cdot frac{sqrt3}{2} - frac{1}{2} cdot frac{sqrt2}{2}=\\= frac{sqrt2}{2}cdot frac{sqrt3-1}{2}=frac{sqrt3-1}{2sqrt2}$