sinA=sinB+cosB、cosA=sinAcosB由(sinB+cosB)^2=1+2sinBcosB得1-cos^2A=sin^2A=1+2cosA=>-cos^2A=2cosA所以只能cosA=0=>cos2A=2cos^2 A-1=2*0-1=-1所以cos^5 2A=-1