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sin(x)+sin2(x)=1
sin2(x)+cos2(x)=1 is a trig identity
sin(x)+sin2(x)=sin2(x)+cos2(x)
sin(x)=cos2(x)
Looking at cos2(x)+cos4(x) we have:
sin(x)+[cos2(x)]2
sin(x)+[sin(x)]2
sin(x)+sin2(x) which equals 1 from your hypothesis above
Therefore cos2(x)+cos4(x)=1 also
 

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