Помогите решить пример пожалуйста[tex] \sqrt{3} cosx - sinx = 1[/tex]. Created by vladsimson. matematika-ru

√3*cosx-sinx=1 | : 2 n∈Z n∈Z n∈Z∈Z

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vladsimson @vladsimson

August 2022 1 5 Report

Помогите решить пример пожалуйста
[tex] \sqrt{3} cosx - sinx = 1[/tex]

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kirichekov

Verified answer

√3*cosx-sinx=1 | : 2
$\frac{ \sqrt{3} }{2}*cosx- \frac{1}{2}*sinx= \frac{1}{2}$
$sin \frac{ \pi }{3}*cosx-cos \frac{ \pi }{3}*sinx= \frac{1}{2}$
$sin( \frac{ \pi }{3}-x )= \frac{1}{2}$
$sin(-(x- \frac{ \pi }{3} ))= \frac{1}{2}$
$-sin(x- \frac{ \pi }{3} )= \frac{1}{2}$
$sin(x- \frac{ \pi }{3} )=- \frac{1}{2}$
$x- \frac{ \pi }{3}= (-1)^{n}*arcsin (-\frac{1}{2})+ \pi n,$ n∈Z
$x-\frac{ \pi }{3} = (-1)^{n+1}*arcsin \frac{1}{2}+ \pi n,$ n∈Z
$x- \frac{ \pi }{3} = (-1)^{n+1}* \frac{ \pi }{6} + \pi n,$ n∈Z
$x= (-1)^{n+1}* \frac{ \pi }{6}+ \frac{ \pi }{3}+ \pi n,$ ∈Z

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