Задача 71251 2sin^2x + 5cosx = -1...

63a199af8597ce7578776f97

05.05.2023 15:15:47

2sin^2x + 5cosx = -1

5f3ea7e3faf909182968ddd9

05.05.2023 19:32:18

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sin^2x=1-cos^2x


2*(1-cos^2x)+5cosx=-1

2cos^2x-5cosx-3=0

D=25-4*2*(-3)=49

cosx=3 или cosx=-1/2


cosx=-1/2

x= ± arccos(-1/2)+2πn, n ∈ [b]Z[/b]

x= ± (π-arccos(1/2))+2πn, n ∈ [b]Z[/b]

x= ± (2π/3)+2πn, n ∈ [b]Z[/b]