[tex] \left \{ {{x-y= \frac{5 \pi }{3} } \atop {Sinx=2Siny}} \right. [/tex]. Created by AvadaKedavra25. algebra-ru

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[tex] \left \{ {{x-y= \frac{5 \pi }{3} } \atop {Sinx=2Siny}} \right. [/tex]

korsukova1234 $\left \{ {{x-y= \frac{5 \pi }{3} } \atop {Sinx=2Siny}} \right.$ ⇒
$\left \{ {{y=x- \frac{5 \pi }{3} } \atop {Sinx=2Sin(x- \frac{5 \pi }{3}} )\right.$

1) $Sinx=2 (Sinx * Cos \frac{5 \pi }{3} - Cosx * Sin \frac{5 \pi }{3} )$
   $Sinx=Sinx+ \sqrt{3}Cosx$
$\sqrt{3} Cosx=0$
   $x= \frac{ \pi }{2} + \pi n, n∈Z$

2) $y=\frac{ \pi }{2} + \pi n - \frac{5 \pi }{3}$
$y=- \frac{7 \pi }{6} + \pi n, n∈Z$

Ответ: $( \frac{ \pi }{2} + \pi n);(- \frac{7 \pi }{6} + \pi n), n∈Z$

2 votes Thanks 2

Grizzly1445 ( Пи\2 + Пи н) (7пи\+ Пи н)

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