已知函数f(x)=（4cos^4x-2cos2x-1）/[sin(π/4+x)·sin^2(π/4-x)]化简

题目

已知函数f(x)=（4cos^4x-2cos2x-1）/[sin(π/4+x)·sin^2(π/4-x)]化简

答案

f(x)=(4cos^4x-2cos2x-1)/[sin(π/4+x)*sin^2(π/4-x)]=(4cos^4x-4cos²x+1)/[sin(π/4)*cosx+sinx*cos(π/4)*(1-cos(π/2-2x))/2]=(2cos²x-1)²/[√2/2*(cosx+sinx)*(1-sin2x)/2]=(cos²x-sin...