( 2cos^2(x)-1 )/(2tan(派/4 -x)*sin^2(派/4+x)化简

2cos^2(x)-1=cos2x
2tan(派/4 -x)*sin^2(派/4+x)
=2tan(派/4 -x)*sin^2[派/2-(派/4-x)]
=2tan(派/4 -x)*cos^2(派/4-x)
=2[sin(派/4 -x)/cos(派/4 -x)]*cos^2(派/4-x)
=2sin(派/4 -x)/cos(派/4 -x)
=sin[2(派/4 -x)]
=sin(派/2 -2x)
=cos2x
所以原式=1