[2(cosx)^4-2(cosx)^2+1/2]/[ 2tan（π/4-x)sin²(π/4+x)]
=1/2*[4(cosx)^4-4(cosx)^2+1]/[ 2tan（π/4-x)sin²(π/4+x)]
=1/2*[2(cosx)^2-1]^2/[ 2tan（π/4-x)sin²(π/4+x)]
=1/2*[2(cosx)^2-1]^2/[ 2tan（π/4-x)sin²(π/4+x)]
=1/2*cos2x/[2tan（π/2-π/4-x)sin²(π/4+x)]
=1/2*cos2x/[2cot（π/4+x)sin²(π/4+x)]
=1/2*cos2x/[2cos（π/4+x)sin(π/4+x)]
=1/2*cos2x/[sin(π/2+2x)]
=1/2*cos2x/cos2x
=1/2