Решите уравнение sin 5x + sin x + 2[tex] sin^{2} [/tex] x = 1. Created by gregorpechorin. algebra-ru

tex] x = 1...

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August 2022 1 9 Report

Решите уравнение

sin 5x + sin x + 2[tex] sin^{2} [/tex] x = 1

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$sin 5x + sin x + 2 sin^{2} x = 1$

$sin5x+sinx=2sin3xcos2x$

$1-2sin^2x=cos2x$

$2sin3xcos2x-cos2x=0$

$cos2x(2sin3x-1)=0$

$cos2x=0 \\ 2x= \pi /2+pi*n \\ x= \pi /4+ \pi n/2 \\\\ 2sin3x-1=0 \\ sin3x=1/2 \\ 3x=(-1)^k* \pi /6+pik \\ x=(-1)^k* \pi /18+ \pi *k/3$

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tex]cos x = 1...

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