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Kent4141
@Kent4141
July 2022
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Решите уравнение. ЧЕРЕЗ Дискрем.
5 sin^2 x - 7 sin x cos x + 4 cos^2 x= 1
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sedinalana
Verified answer
5sin²x-7sinxcosx+4cos²x-sin²x-cos²x=0
4sin²x-7sinxcosx+3cos²x=0/cos²x
4tg²x-7tgx+3=0
tgx=a
4a²-7a+3=0
D=49-48=1
a1=(7-1)/8=0,75⇒tgx=0,75⇒x=arctg0,75+πk,k∈z
a2=(7+1)/8=1⇒tgx=1⇒x=π/4+πk,k∈z
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Answers & Comments
Verified answer
5sin²x-7sinxcosx+4cos²x-sin²x-cos²x=04sin²x-7sinxcosx+3cos²x=0/cos²x
4tg²x-7tgx+3=0
tgx=a
4a²-7a+3=0
D=49-48=1
a1=(7-1)/8=0,75⇒tgx=0,75⇒x=arctg0,75+πk,k∈z
a2=(7+1)/8=1⇒tgx=1⇒x=π/4+πk,k∈z