Question

在△ABC中,abc分别是角ABC的对边,已知b=根号3,B=2π/3,求a+c的最大值

Answer 1

利用正弦定理

a/sinA=c/sinC=b/sinB=√3/(√3/2)=2

a=2sinA,c=2sinC=2sin(60°-A)

a+c

=2sinA+2sin(60°-A)

=2sinA+2sin60°cosA-2cos60°sinA

=sinA+√3cosA

=2[sinA*(1/2)+cosA*(√3/2)]

=2(sinAcos60°+cosAsin60°)

=2sin(A+60°)

当A=30°时,a+c有最大值2