sin^3A+cos^3A=1,求sinA+cosA?
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sin^3A+cos^3A=1,求sinA+cosA?
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^3-3m^2=0,m=0或m=3/2(不合题意,舍去)
所以sinAcosA=0,
2sinAcosA=0,
1+2sinAcosA=1
sin^2A+2sinAcosA+cos^2A=0
(sinA+cosA)^2=1
sinA+cosA=1或-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^3-3m^2=0,m=0或m=3/2(不合题意,舍去)
所以sinAcosA=0,
2sinAcosA=0,
1+2sinAcosA=1
sin^2A+2sinAcosA+cos^2A=0
(sinA+cosA)^2=1
sinA+cosA=1或-1,
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