Помогите пожалуйста решить : [tex]2sin( \frac{7 \pi }{2} -x)*sinx=cosx[/tex]. Created by MrsBrams. algebra-ru

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MrsBrams @MrsBrams

July 2022 1 16 Report

Помогите пожалуйста решить :
[tex]2sin( \frac{7 \pi }{2} -x)*sinx=cosx[/tex]

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Эксперт5

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$2sin( \frac{7 \pi }{2}-x)*sinx=cosx\\\\-2cosx*sinx=cosx\\\\cosx+2sinx*cosx=0\\\\cosx(1+2sinx)=0$

cosx=0 или 1+2sinx=0
x₁=π/2+πn, n∈Z 2sinx=-1
sinx=-1/2
$x_2=(-1)^{n+1}* \pi /6+ \pi n, n\in Z$

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