在△ABC中,已知a^2+b^2=ab=c^2,则sinA+sinB的取值范围是?
5个回答

a^2+b^2=ab+c^2,

所以a^2+b^2-c^2=ab,

cosC=(a^2+b^2-c^2)/2ab=ab/2ab=1/2

所以C=π/3,A+B=2π/3

sinA+sinB

=sinA+sin(A+π/3)

=sinA+1/2sinA+√3/2cosA

=3/2sinA+√3/2cosA

=√3sin(A+π/6)

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