Решить уравнения 1)tg(2x+п/4)= -1 2)√3-tg(x-п/5)=0 3)2sin²x+sinx=0 4)cos²x-2cosx=0. Created by lyricslizergin. algebra-ru

1) ∈ ∈ ∈ ∈ 2) ∈ ∈ ∈ ∈ 3) или или ∈ ∈ ∈ 4) или ∈ или ∅

5)=0 3)2sin²x+sinx=0 4)cos²x-2cosx=0...

lyricslizergin @lyricslizergin

August 2022 1 9 Report

Решить уравнения

1)tg(2x+п/4)= -1

2)√3-tg(x-п/5)=0

3)2sin²x+sinx=0

4)cos²x-2cosx=0

Answers & Comments

Luluput

Verified answer

1)
$tg(2x+ \frac{ \pi }{4} )= -1$
$2x+ \frac{ \pi }{4} =- \frac{ \pi }{4} + \pi n,$ $n$ ∈ $Z$
$2x =- \frac{ \pi }{4}- \frac{ \pi }{4} + \pi n,$ $n$ ∈ $Z$
$2x =- \frac{ \pi }{2} + \pi n,$ $n$ ∈ $Z$
$x =- \frac{ \pi }{4} + \frac{\pi n}{2} ,$ $n$ ∈ $Z$
2)
$\sqrt{3} -tg(x- \frac{ \pi }{5} )=0$
$tg(x- \frac{ \pi }{5} )= \sqrt{3}$
$x- \frac{ \pi }{5}= arctg\sqrt{3} + \pi n,$ $n$ ∈ $Z$
$x- \frac{ \pi }{5}= \frac{ \pi }{3} + \pi n,$ $n$ ∈ $Z$
$x= \frac{ \pi }{3}+ \frac{ \pi }{5} + \pi n,$ $n$ ∈ $Z$
$x= \frac{8 \pi }{15} + \pi n,$ $n$ ∈ $Z$
3)
$2sin^2x+sinx=0$
$sinx(2sinx+1)=0$
$2sinx+1=0$    или    $sinx=0$
$sinx=- \frac{1}{2}$   или    $x= \pi k,$ $k$ ∈ $Z$
$x=(-1)^karcsin(- \frac{1}{2})+ \pi n,$ $n$ ∈ $Z$
$x=(-1)^{k+1} \frac{ \pi }{6}+ \pi n,$ $n$ ∈ $Z$
4)
$cos^2x-2cosx=0$
$cosx(cosx-2)=0$
$cosx=0$   или    $cosx=2$
$x= \frac{ \pi }{2} + \pi n,$ $n$ ∈ $Z$ или ∅

Answers & Comments

Verified answer

4)+1=0...

410 234sin2x10 31 2cosx1 4sinxcosx0 41 2cosx12sin2xcos2x

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