Решить систему уравнений: Sinx+Cosy=-1/2 Sin x Cosy=-1/2. Created by Elfik. matematika-ru

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Настя0271 Нужно сложить уравнения.
т.е получится
косх = 1/2
а дальше легко

4 votes Thanks 2

hELFire

$\left \{ {{\sin x + \cos y=-1/2} \atop {\sin x \cos y=-1/2}} \right.\\ \left \{ {{\sin x =-\cos y-1/2} \atop {(-\cos y-1/2) \cos y=-1/2}} \right.\\ \cos^2y+\frac{1}{2}\cos y - \frac{1}{2}=0\\ \cos y_1 = -1; \cos y_2 = 1/2\\ \sin x_1 = 1/2; \sin x_2 = -1\\ \\ x_1 = 2\pi k \pm\frac{\pi}{6}; y_1 = -\pi + 2\pi k\\ x_2 = =\frac{\pi}{2} + 2\pi k ; y_2 = \frac{\pi}{2} + 2\pi k \pm \frac{\pi}{3}$

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