Question

представьте в виде суммы:
1) $sin23 sin32$
2)$cos\frac{\pi }{12} cos\frac{\pi }{8}$
3)$sin14cos16$
4)$2sin\frac{\pi }{8} cos\frac{\pi }{5}$

Answer 1

$sin23\cdot sin32=\frac{1}{2}\cdot (cos\, 9-cos\, 55)\\\\cos\frac{\pi}{12}\cdot cos\frac{\pi}{8}=\frac{1}{2}\cdot (cos\, \frac{5\pi}{24}+cos\, \frac{\pi}{24})\\\\sin14\cdot cos16=\frac{1}{2}\cdot (sin30+sin(-2))=\frac{1}{2}\cdot (sin30-sin2)\\\\2sin\, \frac{\pi}{8}\cdot cos\, \frac{\pi}{5}=sin\, \frac{13\pi}{40}-sin\, \frac{3\pi}{40}$