cos4x=2cos^2(2x)-1,cos2x=2cos^2(x)-1

cos4x=2(2cos^2(x)-1)^2-1=8cos^4(x) -8cos^2(x) +1=8(cos^4(x)-cos^2(x)) +1

sinx+cosx=1 →1 +2(sinx cosx)=1　→　sinx cosx=0 →sin^2(x)cos^2(x)=0
→cos^2(x)(1-cos^2(x))=0 →cos^4(x)-cos^2(x)=0