已知sin^3A+cos^3A=1,求sinA+cosA的值和sin^4+cos^4的值.
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已知sin^3A+cos^3A=1,求sinA+cosA的值和sin^4+cos^4的值.
已知sin^3A+cos^3A=1,求sinA+cosA的值和sin^4+cos^4的值.
已知sin^3A+cos^3A=1,求sinA+cosA的值和sin^4+cos^4的值.
sin^3A+cos^3A=(sinA+cosA)*(sin^2A+cos^2A-sinAcosA)
=(sinA+cosA)*(1-sinAcosA)=1,
两边平方得:(1+2sinAcosA)*(1-sinAcosA)^2=1,
假设m=sinAcosA,则(1+2m)*(1-m)^2=1,
2m^3-3m^2=0,m=0或m=3/2(不合题意,舍去)
所以sinAcosA=0,
不妨假设:sinA=0,cosA=1或-1,sinA+cosA=1或-1,
sin^4+cos^4=1.