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ytukiya145
@ytukiya145
July 2022
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помогите пожалуйста решить уравнение 1+cos 4x=(2/sinx)
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oganesbagoyan
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Task/24834928
---.---.---.---.---
решить уравнение 1+cos 4x=(2/sinx)
--------
2cos²2x =2 / sinx * * * sinx ≠0 * * *
cos²2x *sinx =1 ; * * * 0≤ cos²2x ≤1 ; - 1≤ sinx ≤1 * * *
⇔{ cos²2x =1 ; sinx =1 .⇔ { (1 -2sin²x)² =1 ; sinx =1 . ⇒sinx =1 ;
x =π/2 +2πn , n∈Z.
ответ : π/2 +2πn , n∈Z.
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Verified answer
Task/24834928---.---.---.---.---
решить уравнение 1+cos 4x=(2/sinx)
--------
2cos²2x =2 / sinx * * * sinx ≠0 * * *
cos²2x *sinx =1 ; * * * 0≤ cos²2x ≤1 ; - 1≤ sinx ≤1 * * *
⇔{ cos²2x =1 ; sinx =1 .⇔ { (1 -2sin²x)² =1 ; sinx =1 . ⇒sinx =1 ;
x =π/2 +2πn , n∈Z.
ответ : π/2 +2πn , n∈Z.