Question

Надо преобразовать в произведение​

Answer 1

$1)\ \ sin10^\circ +sin12^\circ =2\cdot sin\dfrac{10^\circ +12^\circ }{2}\cdot cos\dfrac{10^\circ -12^\circ }{2}=2\cdot sin11^\circ \cdot cos1^\circ \\\\\\2)\ \ sin6^\circ -sin40^\circ =2\cdot sin\dfrac{6^\circ -40^\circ }{2}\cdot cos\dfrac{6^\circ +40^\circ }{2}=-2\cdot sin34^\circ \cdot cos23^\circ \\\\\\3)\ \ cos6^\circ +cos18^\circ =2\cdot cos\dfrac{6^\circ +18^\circ }{2}\cdot cos\dfrac{6^\circ -18^\circ }{2}=2\cdot cos12^\circ \cdot cos6^\circ$

$4)\ \ cos80^\circ -cos20^\circ =-2\cdot sin\dfrac{80^\circ -20^\circ }{2}\cdot sin\dfrac{80^\circ +20^\circ }{2}=-2\cdot sin30^\circ \cdot sin50^\circ =\\\\=-sin50^\circ$

$5)\ \ sin\dfrac{\pi}{10}-sin\dfrac{\pi}{8}=2\cdot sin\dfrac{\frac{\pi}{10}-\frac{\pi}{8} }{2}\cdot cos\dfrac{\frac{\pi}{10}+\frac{\pi}{8}}{2}=2\cdot sin(-\pi)\cdot cos9\pi=0$