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milla25
@milla25
July 2022
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решите уравнение tgx-4ctgx=3
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scTFEKO
Tgx-4ctgx=3
ОДЗ:х≠(πk)/2,k-Z
tgx-4/tgx-3=0 |•tgx
tg²x-3tgx-4=0,Замена:tgx=t
t²-3t-4=0
D=9+16=25=5²
t1=(3+5)/2=4
t2=(3-5)/2=-1
tgx=-1;x1=-π/4+πn,n-Z
tgx=4;x2=arctg4+πm,m-Z
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Answers & Comments
ОДЗ:х≠(πk)/2,k-Z
tgx-4/tgx-3=0 |•tgx
tg²x-3tgx-4=0,Замена:tgx=t
t²-3t-4=0
D=9+16=25=5²
t1=(3+5)/2=4
t2=(3-5)/2=-1
tgx=-1;x1=-π/4+πn,n-Z
tgx=4;x2=arctg4+πm,m-Z