9、f(x)=cosx-1/2cos2x
=cosx-1/2(2cos^2x-1)
=cosx-cos^2x+1/2
=-(cosx-1/2)^2+3/4
最大值：3/4
10、tanA+tanB+tanC=3√3
tanB+tan(A+C)(1-tanAtanC)=3√3
tanB-tanB(1-tan^2B)=3√3
tan^3B=3√3
tanB=(3^3)^(1/6)=√3
B=60°
11、y=sinxcos(x+π/4)+cosxsin(x+π/4)
=sin(x+x+π/4)
=sin(2x+π/4)
T=2π/2=π
12、sin(α+β)sin(β-α)=m
1/2{cos[(α+β)-(β-α)]-cos[(α+β)+(β-α)]}=m
cos2α-cos2β=2m
2cos^2α-1-(2cos^2β-1)=2m
2(cos^2α-cos^2β)=2m
cos^2α-cos^2β=m