第一步到第二步:因为 cos2x=1-2sin^2x
4sin^2(π/4+x)=2*2sin^2(π/4+x)=2[1-cos(π/2+2x)]
f(x)=2[1-cos(π/2+2x)]-2√3cos2x-1 (a)
=2sin2x-2√3cos2x+1 (b)
=4sin(2x-π/3)+1 (c)
(a)到 (b) 因为 公式:cos(π/2+x)=sin x
(b)到(c)因为 公式:sin(x-y)=sinxcosy-cosxsiny
2sin2x-2√3cos2x
=4*[0.5sin2x-0.5√3cos2x]
=4*[sin2xcosπ/3-cos2xsin(π/3)]
=4*sin(2x-π/3)