Question

Срочно помогите дам 100б

Answer 1

$\left\{\begin{array}{l}sinx\cdot siny=\dfrac{3}{4}\\cosx\cdot cosy=\dfrac{1}{4} \end{array}\right\ \ \left\{\begin{array}{l}sinx\cdot siny+cosx\cdot cosy=1\\sinx\cdot siny-cosx\cdot cosy=\dfrac{1}{2}\end{array}\right\ \ \left\{\begin{array}{l}cos(x-y)=1\\-cos(x+y)=\dfrac{1}{2}\end{array}\right$

$\left\{\begin{array}{l}x-y=2\pi n\ ,\ n\in Z\\x+y=\pm \dfrac{2\pi}{3}+2\pi k\ ,\ k\in Z\end{array}\right\ \ \left\{\begin{array}{l}x=y+2\pi n\ ,\ n\in Z\\2y+2\pi n=\pm \dfrac{2\pi}{3}+2\pi k\ ,\ k\in Z\end{array}\right$

$a)\ \left\{\begin{array}{l}x=y+2\pi n\ ,\ n\in Z\\y+\pi n=\dfrac{\pi }{3}+\pi k\ ,\ k\in Z\end{array}\right\ \ b)\ \left\{\begin{array}{l}x=y+2\pi n\ ,\ n\in Z\\y+\pi n=-\dfrac{\pi }{3}+\pi k\ ,\ k\in Z\end{array}\right$

$\left\{\begin{array}{l}x=y+2\pi n\ ,\ n\in Z\\y=\dfrac{\pi}{3}+\pi(k-n)\ ,\ k\in Z\end{array}\right\ \ \ \left\{\begin{array}{l}x=y+2\pi n\\y=-\dfrac{\pi}{3}+\pi (k-n)\ ,\ k\in Z\end{array}\right$

$\left\{\begin{array}{l}x=\dfrac{\pi }{3}+\pi k-\pi n+2\pi n\ ,\ n\in Z\\\ y=\dfrac{\pi}{3}+\pi(k-n)\ ,\ k\in Z\end{array}\right\ \ \ \left\{\begin{array}{l}x=-\dfrac{\pi}{3}+\pi k-\pi n+2\pi n\ ,\ n\in Z\\\ y=-\dfrac{\pi}{3}+\pi (k-n)\ ,\ k\in Z\end{array}\right$

$\left\{\begin{array}{l}x=\dfrac{\pi }{3}+\pi (k+n)\ ,\ n\in Z\\\ y=\dfrac{\pi}{3}+\pi(k-n)\ ,\ k\in Z\end{array}\right\ \ \ \left\{\begin{array}{l}x=-\dfrac{\pi}{3}+\pi (k+n)\ ,\ n\in Z\\\ y=-\dfrac{\pi}{3}+\pi (k-n)\ ,\ k\in Z\end{array}\right$

$Otvet:\ \ \left\{\begin{array}{l}x=\pm \dfrac{\pi }{3}+\pi (k+n)\ ,\ n\in Z\\\ y=\pm \dfrac{\pi}{3}+\pi(k-n)\ ,\ k\in Z\end{array}\right\ .$