Question

Преобразуйте в произведение: cos 5π/12-sin π/12

Answer 1

Ответ:

$cos\dfrac{5\pi}{12}-sin\dfrac{\pi}{12}=cos\dfrac{5\pi}{12}-cos(\pi -\dfrac{\pi}{12})= cos\dfrac{5\pi}{12}-cos\dfrac{11\pi}{12}=\\\\\\=2\cdot sin\dfrac{6\pi}{12}\cdot sin\dfrac{16\pi}{12}=2\cdot sin\dfrac{\pi}{2}\cdot sin\dfrac{4\pi}{3}=2\cdot sin\dfrac{4\pi}{3}=2\cdot sin(\pi+\dfrac{\pi}{3})=\\\\\\=-2\cdot sin\dfrac{\pi}{3}=-2\cdot \dfrac{\sqrt3}{2}=-\sqrt3$