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crazymiku
@crazymiku
July 2022
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Решите уравнение
cos3x*cos2x=cosx
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sedinalana
Verified answer
Cosa*cosb=1/2*(cos(a-b)+cos(a+b))
cosa-cosb=-2sin[(a-b)/2]*sin[(a+b)/2]
-------------------------------------------------------
cos3x*cos2x=cosx
1/2*cosx+1/2*cos5x-cosx=0
1/2*cos5x-1/2*cosx=0
1/2*(cos5x-cosx)=0
1/2*(-2sin2x*sin3x)=0
sin2x=0⇒2x=πnπx=πn/2,n∈z
sin3x=0⇒3x=πn⇒x=πn/3,n∈z
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Answers & Comments
Verified answer
Cosa*cosb=1/2*(cos(a-b)+cos(a+b))cosa-cosb=-2sin[(a-b)/2]*sin[(a+b)/2]
-------------------------------------------------------
cos3x*cos2x=cosx
1/2*cosx+1/2*cos5x-cosx=0
1/2*cos5x-1/2*cosx=0
1/2*(cos5x-cosx)=0
1/2*(-2sin2x*sin3x)=0
sin2x=0⇒2x=πnπx=πn/2,n∈z
sin3x=0⇒3x=πn⇒x=πn/3,n∈z