Question

Помогите решить cos2x*cosx=cos2,5x*cos0,5x

Answer 1

1/2(cosx+cos3x)=1/2(cos2x+cos3x)
cosx+cos3x-cos2x-cos3x=0
cosx-cos2x=0
2sin(x/2)sin(3x/2)=0
sin(x/2)=0⇒x/2=π/2+πn,n∈z⇒x=π+2πn,n∈z
sin(3x/2)=0⇒3x/2=π/2+πk,k∈z⇒x=π/3+2πk/3,k∈z

Answer 2

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