化简函数解析式f(x)=2[sin(π/4+x)]^2-√3cos2x-1,x∈R
问题描述：
化简函数解析式f(x)=2[sin(π/4+x)]^2-√3cos2x-1,x∈R
答
f(x)=2[sin(π/4+x)]^2-√3cos2x-1
=2[√2/2(sinx+cosx)]^2-√3cos2x-1
=1+sin2x-√3cos2x-1
=2(cos(-π/3)sin2x+sin(-π/3)cos2x)
=2sin(2x-π/3)
或者：
f(x)=sin2x-√3cos2x
=2[sin(π/6)sin2x-cos(π/6)cos2x]
=-2cos(2x+π/6)