(1)f(x)=√3coswxsinwx-cos²wx+1/2=√3/2sin2wx-cos2wx/2-1/2+1/2=sin(2wx-π/6)
依题意可得,T/2=π,则T=2π/2w=2π,w=1/2
(2)f(x)=sin(x-π/6),则f(C)=1/2有C-π/6=π/6或5π/6,显然C=π/3.
cosC=(a²+b²-c²)/2ab=1/2,有a²+b²-76=ab
又有S△ABC=2√3=1/2absinC=√3ab/4,有ab=8
(a+b)²=a²+b²+2ab=76+ab+2ab=76+24=100
推出a+b=10(-10舍去)