1.
f(x)=2cos^2 wx/2+cos(wx+π/3)-1=coswx+cos(wx+π/3)=2cos(wx+π/6)•cos(π/6)=cos(wx+π/6)
|AB|=|x1-x2|=π/w=π/2
w=2
f(x)=cos(2x+Pai/6)
2
f(A)=-3/2
cos(2A+π/6)=-√3/2
2A+Pai/6=5Pai/6
A=Pai/3
S=1/2bcsinA=1/2b*3sinPai/3=3根号3
故有b=4
a^2=b^2+c^2-2bccosA=16+9-2*4*3*1/2=13
a= 根号13