Задача 73776 cosx + 2cos2x = 1...

653c8456df8de70c102f46f7

28.10.2023 06:49:11

cosx + 2cos2x = 1

5f3ea7e3faf909182968ddd9

28.10.2023 13:50:14

★

[m]cosx+2*(cos^2x-sin^2x)=cos^2x+sin^2x[/m]

[m]cosx+2*cos^2x-cos^2x-2sin^2x-sin^2x=0[/m]

[m]cosx+cos^2x-3*sin^2x=0[/m]

[m]cosx+cos^2x-3*(1-cos^2x)=0[/m]

[m]4cos^2x+cosx-3=0[/m]

Квадратное уравнение.

cosx=t

4t^2+t-3=0

D=1-4*4*(-3)=49

t_(1)=-1 или t_(2)=3/4


cosx=-1 или cosx=3/4


x=π+2πk, k ∈ [b]Z[/b] или x=arccos(3/4)+2πn, n ∈ [b]Z[/b]