Тригонометрическое уравнение [tex]4(1-cosx)=3sin\frac{x}{2}cos^2\frac{x}{2}[/tex]. Created by karavanov1. algebra-ru

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karavanov1 @karavanov1

July 2022 1 25 Report

Тригонометрическое уравнение
[tex]4(1-cosx)=3sin\frac{x}{2}cos^2\frac{x}{2}[/tex]

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NNNLLL54

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Формула: $sin^2\frac{x}{2}=\frac{1-cosx}{2}\; \; \Rightarrow \; \; 1-cosx=2sin^2\frac{x}{2}$ .

$4(1-cosx)=3sin\frac{x}{2}cos^2\frac{x}{2}\\\\4\cdot 2sin^2\frac{x}{2}-3sin\frac{x}{2}cos^2\frac{x}{2}=0\\\\sin\frac{x}{2}\cdot (8sin\frac{x}{2}-3cos^2\frac{x}{2})=0\\\\a)\; sin\frac{x}{2}=0\; ,\; \; \frac{x}{2}=\pi n\; ,\; \; x=2\pi n\; ,\; n\in Z\\\\b)\; \; 8sin\frac{x}{2}-3(1-sin^2\frac{x}{2})=0\\\\3sin^2\frac{x}{2}+8sin\frac{x}{2}-3=0\\\\D/4=4^2-3\cdot (-3)=25\\\\sin\frac{x}{2}=\frac{-4-5}{3}=-3\ \textless \ 1\; \; net\; reshenij\; ,t.k.\; |sin \alpha | \leq 1$

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tex kak my poluchili x x 242 ponyatno chto skobki x 4 sokratilis delo ne

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zaputalsya pomogite s trigonometriej vot cos80 kakoe iz preobrazovanij schitaet

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mozhno li najti pervoobraznuyu bez pomoshi tablicy tolko nachal prohodit temu per

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tex da v dannom primere ne bylo raznicy vozmi ya 1 ili 1 tk vo vtoroj

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