Question

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Решите систему уравнений: x-y=π/6,
cosx*siny=1/4

Answer 1

Объяснение:

$\left\{\begin{array}{ccc}x-y=\frac{\pi }{6} \\cosx*siny=\frac{1}{4} \\\end{array}\right\ \ \ \ \ \left\{\begin{array}{ccc}x=\frac{\pi }{6}+y \\siny*cos(\frac{\pi }{6} +y)=\frac{1}{4} \\\end{array}\right\ \ \ \ \ \ \ \ \ \Rightarrow\\siny*cos(\frac{\pi }{6}+y)=\frac{1}{4} \\\frac{1}{2}*(sin(y-\frac{\pi }{6} -y)+sin(y+\frac{\pi }{6}+y)=\frac{1}{4}\ |*2\\sin(-\frac{\pi }{6})+sin(\frac{\pi }{6} +2y)=\frac{1}{2}\\-\frac{1}{2} +sin(\frac{\pi }{6} +2y)=\frac{1}{2} \\sin(\frac{\pi }{6}+2y)=1\\$

$\frac{\pi }{6}+2y=\frac{\pi }{2}+2\pi n\\2y=\frac{\pi }{3}+2\pi n\ |:2\\y=\frac{\pi }{6}+\pi n.\ \ \ \ \Rightarrow\\x=\frac{\pi }{6}+\frac{\pi }{6} +\pi n\\x=\frac{\pi }{3} +\pi n.$

ответ: x=π/3+πn,   y=x/6+πn.