[(1+sinx+cosx)/(1+sinx-cosx)]+[(1+sinx-cosx)/(1+sinx+cosx)]
=(1+sinx+cosx)^2+(1+sinx-cosx)^2/(1+sinx)^2-cos^2x
=2(1+sinx)^2+2cos^2x/(1+sinx)^2-cos^2x
=4+4sinx/2sinx+2sin^2x
=4/2sinx
=2/sinx