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ghostnight01
@ghostnight01
August 2022
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3 ctg x - 2 tg x - 1 = 0
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Spilrobe
3ctgx -2tgx-1=0
3ctgx-2tgx-tgxctgx=0
3×cosx/sinx - 2×sinx/cosx - cosxsinx/sinxcosx=0
3×cos^(2)x-2×sin^(2)x-cosxsinx/sinxcosx=0
Домножаем все на sinxcosx
3×cos^(2)x-2×sin^(2)x-cosxsinx=0
Делим все на cos^(2)x
3-2×tg^(2)x-tgx=0
2tg^(2)x+tgx-3=0
Замена tgx=t
2t^2+t-3=0
Д=5^2
T1=1
T2=-3/2
[tgx=1
[tgx=-3/2
[x=П/4 + Пк, к € Z
[x=-arctg3/2 +Пm, m € Z
2 votes
Thanks 2
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Answers & Comments
3ctgx-2tgx-tgxctgx=0
3×cosx/sinx - 2×sinx/cosx - cosxsinx/sinxcosx=0
3×cos^(2)x-2×sin^(2)x-cosxsinx/sinxcosx=0
Домножаем все на sinxcosx
3×cos^(2)x-2×sin^(2)x-cosxsinx=0
Делим все на cos^(2)x
3-2×tg^(2)x-tgx=0
2tg^(2)x+tgx-3=0
Замена tgx=t
2t^2+t-3=0
Д=5^2
T1=1
T2=-3/2
[tgx=1
[tgx=-3/2
[x=П/4 + Пк, к € Z
[x=-arctg3/2 +Пm, m € Z