# Find the general solution for the equation cos 4 x = cos 2 x

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Find the general solution for each of the following equations:

1. cos 4 x = cos 2 x

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Solution:

cos4x=cos2x
cos2x−cos4x=0
−2sin(2x+4x)/2.sin(2x−4x)/2 = 0
−2sin3x.sin(−x)=0
2sin3x.sinx=0
If sin3x=0
⇒3x=nπ
⇒x=nπ/3
sinx=0
⇒x=nπ where n∈z

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