(1)
m//n
=>
2sinB/(-√3 ) = cos2B/(2[cos(B/2)]^2-1)
2sinB(2[cos(B/2)]^2-1) =-√3cos2B
sin2B = -√3cos2B
tan2B = -√3
B = π/3
(2)
b=2
by sine-rule
a/sinA = b/sinB
a= (b/sinB)sinA = (4√3/3)sinA
c= (b/sinB)sinC = (4√3/3)sinC = (4√3/3)sin(2π/3-A)
A1= 三角形ABC的面積
= (1/2)ac sinB
= (1/2)(4√3/3)sinA .(4√3/3)sin(2π/3-A) (√3/2)
= (4/3)sinAsin(2π/3-A)
= (2/3)[cos(2A-2π/3)-cos(2π/3)]
=(2/3)[cos(2A-2π/3)+1/2]
max A1 at A=π/3
=(2/3)[1+1/2]
=1