Известно, что sin x = 3/2sin y - 2/3cos y, cos x = 3/2cos y - 2/3sin y. Найдите sin2y. Created by AEAakimova. matematika-ru

3sin y. Найдите sin2y...

AEAakimova @AEAakimova

June 2022 1 3 Report

Известно, что sin x = 3/2sin y - 2/3cos y, cos x = 3/2cos y - 2/3sin y. Найдите sin2y

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$sinx= \frac{3}{2} sin y - \frac{2}{3} cos y$
$cosx= \frac{3}{2} cos y - \frac{2}{3} sin y$
$sin2y-$ ?

$sinx= \frac{3}{2} sin y - \frac{2}{3} cos y$
*
$cosx= \frac{3}{2} cos y - \frac{2}{3} sin y$
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$sinx*cosx=(\frac{3}{2} sin y - \frac{2}{3} cos y)*( \frac{3}{2} cos y - \frac{2}{3} sin y)$
$sinx*cosx=\frac{9}{4} sin y*cosy-sin^2y-cos^2y+ \frac{4}{9} cos y}*sin y$
$sinx*cosx=\frac{81}{36} sin y*cosy-(sin^2y+cos^2y)+ \frac{16}{36} cos y}*sin y$
$sinx*cosx=\frac{97}{36} sin y*cosy-1$
$0.5sin2x=\frac{97}{36} sin y*cosy-1$
$\frac{97}{36} sin y*cosy=0.5sin2x+1$
$sin y*cosy=(0.5sin2x+1):\frac{97}{36}$
$sin y*cosy=(0.5sin2x+1)*\frac{36}{97}$
$sin y*cosy= \frac{18sin2x+36}{97}$

$sin2y=2siny*cosy$
$sin2y=2* \frac{18sin2x+36}{97}$
$sin2y=\frac{36sin2x+72}{97}$

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3sin y najdite sin2y

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3sin y najdite sin2y

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