已知函数f(x)=(1+1/tanx)sin^2-2sin(x+π/4)sin(x-π/4).求tana=2时,f(a)若x属于〔_数学解答

已知函数f(x)=(1+1/tanx)sin^2-2sin(x+π/4)sin(x-π/4).求tana=2时,f(a)
若x属于〔π/12,π/2〕,求f(x)的取值范围

人气：156 ℃　时间：2019-08-21 08:46:38

解答

,而sin^2a+cos^2a=1,得sin^2a=4/5f(x)=(1+1/tanx)sin^2-2sin(x+π/4)sin(x-π/4).=sinx(cosx+sinx)+2sin(x+π/4)cos(x+π/4)=1/2sin2x+sin^2x+sin(2x+π/2)=1/2sin2x+1/2-1/2cos2x+cos2x=(sin2x+cos...