Question

один примерчик умоляю (((
Упростить : Sin п/7 cos 4п/21 +sin 4п/21 cos п/7​

Answer 1

Объяснение:

$sin\frac{\pi }{7}*cos\frac{4\pi }{21} +sin\frac{4\pi }{21}*cos\frac{\pi }{7}=\\=\frac{1}{2}*(sin(\frac{\pi }{7}-\frac{4\pi }{21})+sin(\frac{\pi }{7} +\frac{4\pi }{21}))+ \frac{1}{2}*(sin(\frac{4\pi }{21}-\frac{\pi }{7})+sin(\frac{4\pi }{21}+\frac{\pi }{7}))=\\=\frac{1}{2}*(sin(-\frac{\pi }{21} )+sin\frac{\pi }{3})+\frac{1}{2} *(sin\frac{\pi }{21}+ sin\frac{\pi }{3} )=\\$

$=\frac{1}{2}*(-sin\frac{\pi }{21} +sin\frac{\pi }{3}+ sin\frac{\pi }{21}+sin\frac{\pi }{3} )=\frac{1}{2}*2*sin\frac{\pi }{3} =sin\frac{\pi }{3}=\frac{\sqrt{3} }{2}.$