Ответы и объяснения

2013-06-15T18:14:06+04:00

\left \{ {{x-y=\pi} \atop {-2sin\frac{x+y}{2}sin\frac{x-y}{2}=\sqrt3}} \right.

\left \{ {{x-y=\pi} \atop {sin\frac{x+y}{2}sin\frac{\pi}{2}=-\frac{\sqrt3}{2}} \right.

\left \{ {{x-y=\pi} \atop {sin\frac{x+y}{2}=-\frac{\sqrt3}{2}} \right.

\left \{ {{x-y=\pi} \atop {\frac{x+y}{2}=(-1)^k\frac{\pi}{3}+\pi k} \right.

Данная система равносильна совокупности систем:

\left \{ {{x-y=\pi} \atop {\frac{x+y}{2}=-\frac{\pi}{3}+2\pi k} \right. или \left \{ {{x-y=\pi} \atop {\frac{x+y}{2}=-\frac{2\pi}{3}+2\pi n} \right.

\left \{ {{x-y=\pi} \atop {x+y=-\frac{2\pi}{3}+4\pi k} \right. или \left \{ {{x-y=\pi} \atop {x+y=-\frac{4\pi}{3}+4\pi n} \right.

Решая каждую систему способом сложения, получим:

\left \{ {{x-y=\pi} \atop {x=\frac{\pi}{6}+2\pi k} \right. или \left \{ {{x-y=\pi} \atop {x=-\frac{\pi}{6}+2\pi n} \right.

\left \{ {{y=-\frac{5\pi}{6}+2\pi k} \atop {x=\frac{\pi}{6}+2\pi k} \right. или \left \{ {{y=-\frac{7\pi}{6}+2\pi n} \atop {x=-\frac{\pi}{6}+2\pi n} \right.

Ответ: (\frac{\pi}{6}+2\pi k; -\frac{5\pi}{6}+2\pi k)(-\frac{\pi}{6}+2\pi n; -\frac{7\pi}{6}+2\pi n)