(1)根据正弦定理a/sinA=c/sinC,代入可得 根号3sinCsinA=sinAcosC
由于0由于0
=(根号3)cosA+cos150cosA+sin150sinA
=(根号3)cosA-1/2(根号3)cosA+1/2sinA
=sin(60+A)
由于60<60+A<210,故60+A=90,即A=30度时有最大值
此时A=C,故三角形ABC为等腰三角形
a/sinA=c/sinC,把这个式子代入得(根号3)asinC=acosC可以求得tanC=根号3/3,所以C=30度
√3csinA =acosC
√3sinCsinA =sinAcosC
√3sinC =cosC
tanC=√3/3
C=π/6
2)√3cosA +cosB=√3cosA +cos(5π/6-A)
=√3cosA -√3/2*cosA+1/2*sinA
=√3/2*cosA+1/2*sinA
=sin(A+π/3)
取最大值时有:A+π/3=π/2
A=π/6
A=C=π/6
△ABC是等腰三角形