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karinabzaeva
@karinabzaeva
July 2022
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Помогите решить
4sin^2+cos^2+5sinx*cosx=0
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kirichekov
Verified answer
4sin²x+cos²x+5sinx*cosx=0 |:cos²x≠0
4sin²x/cos²x+cos²x/cos²x+5sinx*cosx/cos²x=0
4tg²x+1+5tgx=0
tgx=y
4y²+5y+1=0
a=4, b=5, c=1
D=5²-4*4*1=9
y₁,₂=(-b+-√D)/(2*a)
y₁=(-5-3)/8, y₁=-1
y₂=(-5+3)/8, y₂=-1/4
1. y=-1, tgx=-1,
x₁=-πn, n∈Z
2. y=-1/4, tgx=-1/4,
x₂=-arctg(1/4)+πn, n∈Z
0 votes
Thanks 1
karinabzaeva
извини за вопрос, но почему в y -5
kirichekov
понятно теперь?
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Answers & Comments
Verified answer
4sin²x+cos²x+5sinx*cosx=0 |:cos²x≠04sin²x/cos²x+cos²x/cos²x+5sinx*cosx/cos²x=0
4tg²x+1+5tgx=0
tgx=y
4y²+5y+1=0
a=4, b=5, c=1
D=5²-4*4*1=9
y₁,₂=(-b+-√D)/(2*a)
y₁=(-5-3)/8, y₁=-1
y₂=(-5+3)/8, y₂=-1/4
1. y=-1, tgx=-1, x₁=-πn, n∈Z
2. y=-1/4, tgx=-1/4, x₂=-arctg(1/4)+πn, n∈Z