Question

Даю 100 балів

допоможіть розвязати систему
cos(x)*cos(y)+sin(x)*sin(y)=0.5
sin(x)*cos(y)+cos(x)*sin(y)=1

Answer 1

$\displaystyle \left \{ {{cosx*cosy+sinx*siny=0.5} \atop {sinx*cosy+cosx*siny=1}} \right.\\\\\left \{ {{cos(x-y)=0.5} \atop {sin(x+y)=1}} \right. \\\\sin(x+y)=1\\\\x+y=\frac{\pi }{2}+2\pi n; n \in Z\\\\x=\frac{\pi }{2}-y+2\pi n; n \in Z\\\\ cos(x-y)=0.5\\\\cos(\frac{\pi }{2}+2\pi n-y-y)=0.5\\\\cos(\frac{\pi }{2}-2y)=0.5\\\\sin(2y)=0.5\\\\2y= \frac{\pi }{6}+2\pi n; n \in Z; ili: 2y=\frac{5\pi }{6}+2\pi n; n \in Z$

$\displaystyle y_1=\frac{\pi }{12}+\pi n; x_1=\frac{\pi }{2}-\frac{\pi }{12}-\pin+2\pi n=\frac{5\pi }{12}+\pi n; n\in Z\\\\y_2=\frac{5\pi}{12}+\pi n; x_2=\frac{\pi }{2}-\frac{5\pi }{12}-\pi n+2\pi n=\frac{\pi }{12}+\pi n; n \in Z$