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maaaaaaarusya
@maaaaaaarusya
August 2022
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tg(x+pi/4) + tg (x - pi/4) = tg x
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Answers & Comments
rskopov
Решение:
sin(x+pi/4+x-pi/4)/cos(x-pi/4)cos(x+pi/4)=sinx/cosx
4sinxcosx/cos2x=sinx/cosx
sinx=0
x=Пk
4cosx=cos2x
4cosx=2cos^2x-1
(2+-sqrt(6))/2
1+sqrt(6)/2>1
(1-sqrt(6)/2>-1
нет решения
Ответ: x=Пk.
2 votes
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Answers & Comments
sin(x+pi/4+x-pi/4)/cos(x-pi/4)cos(x+pi/4)=sinx/cosx
4sinxcosx/cos2x=sinx/cosx
sinx=0
x=Пk
4cosx=cos2x
4cosx=2cos^2x-1
(2+-sqrt(6))/2
1+sqrt(6)/2>1
(1-sqrt(6)/2>-1
нет решения
Ответ: x=Пk.