tex]...

ждлорп @ждлорп

July 2022 1 10 Report

[tex] \left \{ {{ \frac{sinx}{siny} =1} \atop {x-y= \frac{\pi}{3 }} \right. [/tex]

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Artem112

Verified answer

$\left \{ {{ \frac{sinx}{siny} =1} \atop {x-y= \frac{\pi}{3 }} \right. 
\\\
 \left \{ {{ sinx=siny} \atop {x=y+ \frac{\pi}{3 }} \right. 
\\\
sin(y+ \frac{\pi}{3 })=siny
\\\
sinycos\frac{\pi}{3 }+cosysin\frac{\pi}{3 }=siny
\\\
 \frac{1}{2} siny+ \frac{ \sqrt{3} }{2}cosy=siny
\\\
 \frac{1}{2} siny- \frac{ \sqrt{3} }{2}cosy=0
\\\
siny- \sqrt{3} cosy=0
\\\
tg y-\sqrt{3}=0
\\\
y= \frac{\pi}{3}+\pi n , n\in Z
\\\
x= \frac{\pi}{3}+ \frac{\pi}{3}+\pi k= \frac{2\pi}{3}+\pi k, k\in Z$

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