Question

Преобразуйте в произведение

sin11п/12 + sin5п/12

Answer 1

Ответ:

$\frac{\sqrt{6} }{2}$

Пошаговое объяснение:

$sin(a ) + sin(b )=2sin(\frac{a+b}{2})cos(\frac{a-b}{2}) )\\sin(\frac{11\pi }{12} ) + sin(\frac{5\pi }{12} )=\\2sin(\frac{\frac{11\pi}{12}+ \frac{5\pi}{12}}{2} )cos(\frac{\frac{11\pi}{12}- \frac{5\pi}{12}}{2} )=\\\\2sin(\frac{16\pi}{12*2})cos({\frac{6\pi}{12*2})=\\\\2sin(\frac{2\pi}{3})cos({\frac{\pi}{4})=\\2*\frac{\sqrt{3}\2}{2}*\frac{\sqrt{2} }{2} =\frac{\sqrt{6} }{2}$