设函数f(x)=cos(2x+π/3)+(sinx)2.(1)求函数f(x)的最大值和最小正周期 (2)设A.B.C为三

(1)f(x)=cos(2x+π/3)+(sinx)2
sinx^2=(1-cos2x)/2
f(x)=1/2cos2x-√3/2sin2x+1/2-1/2cos2x
=-√3/2sin2x+1/2
最大值是√3/2+1/2
最小值是-√3/2+1/2
周期T=2π/2=π
(2)f(C/2)=-√3/2sinC+1/2=－1/4
sinC=√3/2
且C为锐角则C=π/3
cosC=1/2
cosB=1/3.sinB=2√2/3
sinA=sin(B+C)=sinBcosC+sinCcosB
=2√2/3*1/2+√3/2*1/3
=(√3+2√2)/6