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dienstag
@dienstag
July 2022
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Математика, тригонометрические уравнения. 6cos^2x+4sinxcosx=1 и аналогичное 5cos^2x+3sinxcosx=1
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sedinalana
Verified answer
6cos²x+4sinxcosx-sin²x-cos²x=0/cos²x
tg²x-4tgx-5=0
tgx=a
a²-4a-5=0
a1+a2=4 U a1*a2=-5
a1=-1⇒tgx=-1⇒x=-π/4+πn,n∈z
a2=5⇒tgx=5⇒x=arctg5+πk,k∈z
5cos²x+3sinxcosx-sin²x-cos²x=0/cos²x
tg²x-3tgx-4=0
tgx=a
a²-3a-4=0
a1+a2=3 U a1*a2=-4
a1=-1⇒tgx=-1⇒x=-π/4+πn,n∈z
a2=4⇒tgx=4⇒x=arctg4+πk,k∈z
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Answers & Comments
Verified answer
6cos²x+4sinxcosx-sin²x-cos²x=0/cos²xtg²x-4tgx-5=0
tgx=a
a²-4a-5=0
a1+a2=4 U a1*a2=-5
a1=-1⇒tgx=-1⇒x=-π/4+πn,n∈z
a2=5⇒tgx=5⇒x=arctg5+πk,k∈z
5cos²x+3sinxcosx-sin²x-cos²x=0/cos²x
tg²x-3tgx-4=0
tgx=a
a²-3a-4=0
a1+a2=3 U a1*a2=-4
a1=-1⇒tgx=-1⇒x=-π/4+πn,n∈z
a2=4⇒tgx=4⇒x=arctg4+πk,k∈z