f(A)=2cosA/2sin(π-A/2)+sin²A/2-cos²A/2
=2cosA/2*sinA/2-(cos²A/2-sin²A/2)
=sinA-cosA
=√2sin(A-π/4)
(1)f(A)的最大值=√2
(2)
f（A）=0
sin(A-π/4)=0
A是内角
A=π/4
C=5π/12
B=π-π/4-5π/12=π/3
应用正弦定理
a/sinA=b/sinB
√6/(√2/2)=b/(√3/2)
b=3