Prove that cos4x = cos2x

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Solution

cos4x=cos2x
2cos22x-1=cos2x
2cos22x-cos2x-1=0
2cos22x-2cos2x+cos2x-1=0
2cos2x(cos2x-1)+1(cos2x-1)=0
(cos2x-1)(2cos2x+1)=0

$cos 2 x minus 1 equals 0 space o r space 2 cos 2 x plus 1 equals 0 cos 2 x equals 1 space o r space cos 2 x equals fraction numerator negative 1 over denominator 2 end fraction 2 x equals 0 space o r space 2 x equals 120 x equals 0 space o r space x equals space 60 s o space w h e n space x space h a s space a b o v e space v a l u e s cos 4 x space equals cos 2 x$

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