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loverov
@loverov
July 2022
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6sin^2x-3sinxcosx-cos^2x=1
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EmiliedeRavin
6sin²x-3sinxcosx-cos²х=1
6sin²x-3sinxcosx-cos²х=sin²x+cos²х
6sin²x-3sinxcosx-cos²х-sin²x-cos²х=0
5sin²x-3sinxcosx-2cos²х=0 I :cos²х
5tg²x-3tgx-2=0
Введем новую переменную:
tgx=a
5a²-3a-2=0
D=9+40=49=7²
a1=(3+7)/10=1
a2=(3-7)/10=-2/5
Возвращаемся к замене:
tgx=1 tgx=-2/5
x=π/4+πn, n∈z x=-arctg2/5 + πn, n∈z
18 votes
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Answers & Comments
6sin²x-3sinxcosx-cos²х=sin²x+cos²х
6sin²x-3sinxcosx-cos²х-sin²x-cos²х=0
5sin²x-3sinxcosx-2cos²х=0 I :cos²х
5tg²x-3tgx-2=0
Введем новую переменную:
tgx=a
5a²-3a-2=0
D=9+40=49=7²
a1=(3+7)/10=1
a2=(3-7)/10=-2/5
Возвращаемся к замене:
tgx=1 tgx=-2/5
x=π/4+πn, n∈z x=-arctg2/5 + πn, n∈z