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xomka012
@xomka012
July 2022
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Найдите все решения уравнения:
(sin²x+1)cosx = 2-cos²x
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sangers
(sin²x+1)*cosx=2-cos²x
(sin²x-1+1+1)*cosx=2-cos²x
(-cos²x+2)*cosx=2-cos²x
-cos³x+2*cosx=2-cos²x
cos³x-cos²x-2*cosx+2=0
Пусть cosx=|t |≤1 ⇒
t³-t²-2t+2=0
t(t-1)-2*(t-1)=0
(t-1)*(t-2)=0
t-1=0 t₁=1 cosx=1 x=2πn
t-2=0 t₂=2 ∉
Ответ: x=2πn.
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Answers & Comments
(sin²x-1+1+1)*cosx=2-cos²x
(-cos²x+2)*cosx=2-cos²x
-cos³x+2*cosx=2-cos²x
cos³x-cos²x-2*cosx+2=0
Пусть cosx=|t |≤1 ⇒
t³-t²-2t+2=0
t(t-1)-2*(t-1)=0
(t-1)*(t-2)=0
t-1=0 t₁=1 cosx=1 x=2πn
t-2=0 t₂=2 ∉
Ответ: x=2πn.