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August 2022
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3sin2x -2sinxcosx – 1=0
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oganesbagoyan
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Task/22875706
---.---.---.---.---.---
3sin2x -2sinxcosx – 1=0 ;
3*2sinxcosx -2sinxcosx –(sin²x +cos²x)
=0 ;
sin²x - 4sinxcosx + cos²x =0 || : cos²x ≠ 0
tg²x -4tgx +1 =0 * * * tg= t
t² - 4t +1 =0 D/4 =(4/2)² -1 =√3
t₁ =2 -√3 ⇒ tgx₁= 2 -√3 ; x₁= arctg(2 -√3) +πn , n∈Z ;
t₂ =2+√3 ⇒ tgx₂ =2+√3 ; x₂= arctg(2 +√3) +πn , n∈Z .
ответ : arctg(2 -√3) +πn , arctg(2 +√3) +
πn ,
n∈Z.
.
1 votes
Thanks 1
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Verified answer
Task/22875706---.---.---.---.---.---
3sin2x -2sinxcosx – 1=0 ;
3*2sinxcosx -2sinxcosx –(sin²x +cos²x)=0 ;
sin²x - 4sinxcosx + cos²x =0 || : cos²x ≠ 0
tg²x -4tgx +1 =0 * * * tg= t
t² - 4t +1 =0 D/4 =(4/2)² -1 =√3
t₁ =2 -√3 ⇒ tgx₁= 2 -√3 ; x₁= arctg(2 -√3) +πn , n∈Z ;
t₂ =2+√3 ⇒ tgx₂ =2+√3 ; x₂= arctg(2 +√3) +πn , n∈Z .
ответ : arctg(2 -√3) +πn , arctg(2 +√3) +πn , n∈Z. .