已知：TAN（π/4+a)=1/2

tan(π/4+a)=1/2
(tanπ/4+tana)/(1-tanπ/4tana)=1/2
(1+tana)/(1-tana)=1/2
1-tana=2(1+tana)
3tana=-1
tana=-1/3
(sin2a-cos^2a)/(1+cos2a)
=(sin2a-cos^2a)/(1+2cos^2a-1)
=(sin2a-cos^2a)/(2cos^2a)
=(2sinacosa-cos^2a)/(2cos^2a)
=(2sina-cosa)/(2cosa)
=2sina/2cosa-cosa/2cosa
=tana-1/2
=-1/3-1/2
=-5/6