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Prove that (1+sinx-cosx)/(1+sinx +cosx)+...

Prove that `(1+sinx-cosx)/(1+sinx +cosx)+(1+sinx+cosx)/(1+sinx-cosx)=2 cosecx`

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`L.H.S. = (1+sinx-cosx)/(1+sinx+cosx)+(1+sinx+cosx)/(1+sinx-cosx)`
`=((1+sinx-cosx)^2+(1+sinx+cosx)^2)/((1+sinx+cosx)(1+sinx-cosx))`
`=((1+sinx)^2+cos^2x-2(1+sinx)cosx+(1+sinx)^2+cos^2x+2(1+sinx)cosx)/((1+sinx)^2-cos^2x)`
`=(1+sin^2x+2sinx+cos^2x+1+sin^2x+2sinx+cos^2x)/(1+sin^2x+2sinx-cos^2x)`
`= (1+4sinx+(sin^2x+cos^2x)+1+(sin^2x+cos^2x))/(2sinx+sin^2x+(1-cos^2x))`
`=(4+4sinx)/(2sinx+sin^2x+sin^2x)`
`=(4(1+sinx))/(2sinx(1+sinx))`
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