(sinx)^6+(cosx)^6

express (sinx)^6+(cosx)^6 in terms of A+Bcos4x

here is my steps, which one should i amend?

define sinx=s cosx=c

s^6+c^6=(s^4)-( sc )^2+c^4
=(1-2( sc )^2) - (sc)^2
=1-3(sc)^2

consider cos4x=cos( 2(2x) )=1-2( sin2x )^2=1-2( 2sc )^2=1-8(sc)^2


so s^6+c^6=1-3(sc)^2=cos4x+5(sc)^2= ???

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or show me your steps.
thz