sin^3A+cos^3A=1,求sinA+cosA?
问题描述:
sin^3A+cos^3A=1,求sinA+cosA?
答
sin^3A+cos^3A=1(sinA+cosA)(sin^2A-sinAcosA+cos^2A)=1(sinA+cosA)(1-sinAcosA)=1两边平方得:(sin^2A+2sinAcosA+cos^2A)*(1-sinAcosA)^2=1,(1+2sinAcosA)*(1-sinAcosA)^2=1,设m=sinAcosA,则(1+2m)*(1-m)^2=1,2m^3...