(1) f(x)=sin(π/2-x)-√3sin(π-x)
=2(1/2cosx-√3/2sinx)
=2(sinπ/6cosx-sinxcosπ/6)
=2sin(π/6-x)
T=2π/w=2π
f(x)max=2
f(x)min=-2
∴f(x)∈[-2,2]
2) f(a-π/3)=-2/3
2sin(π/6-a+π/3)=2sin(π/2-a)=2cosa
∴cosa=-1/3
∴cos2a/(1+cos2a-sin2a)=（2cos²a-1）/(1+2cos²a-1-2sinacosa)
sina=√(1-cos²a)=2√2/3
代入后原式=1/2-√2