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maridovnar
@maridovnar
June 2022
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1 - cosX = tgX - sinX
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sangers1959
Verified answer
1-cosx=tgx-sinx
1-cosx=(sinx/cosx)-sinx ОДЗ: сosx≠0 x≠π/2+πn.
1-cosx=sinx*(1/cosx-1)
sinx*(1-cosx)/cosx-(1-cosx)=0
(1-cosx)*(tgx-1)=0
1-cosx=0
cosx=1
x₁=2πn
tgx-1=0
tgx=1
x₂=π/4+πn.
Ответ: x₁=2πn x₂=π/4+πn.
[-2π;3π] x=-2π; 0; 2π; -7π/4; -3π/4; π/4; 5π/4; 9π/4; 13π/4.
13 votes
Thanks 13
maridovnar
Спасибо огромное
maridovnar
помогите пожалуйста найти количество корней на промежутке от минус 2пи до 3 пи
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Answers & Comments
Verified answer
1-cosx=tgx-sinx1-cosx=(sinx/cosx)-sinx ОДЗ: сosx≠0 x≠π/2+πn.
1-cosx=sinx*(1/cosx-1)
sinx*(1-cosx)/cosx-(1-cosx)=0
(1-cosx)*(tgx-1)=0
1-cosx=0
cosx=1
x₁=2πn
tgx-1=0
tgx=1
x₂=π/4+πn.
Ответ: x₁=2πn x₂=π/4+πn.
[-2π;3π] x=-2π; 0; 2π; -7π/4; -3π/4; π/4; 5π/4; 9π/4; 13π/4.