cos4α=1-2(sin2α)^2=1-8(sinα)^2*(cosα)^2=1-8(sinα)^2*[1-(sinα)^2]=8(sinα)^4-8(sinα)^2+1而4cos2α+8(sinα)^4-3=4[1-2(sinα)^2]+8(sinα)^4-3=8(sinα)^4-8(sinα)^2+1所以cos4α=4cos2α+8(sinα)^4-3即3+cos4α-4cos2α=8sinα^4
