cosecx/cosecx-1+cosecx/cosecx+1= 2sec²x
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cosecx/cosecx-1+cosecx/cosecx+1
=(cosecx(cosecx+1)+ cosecx(cosecx-1))/cosecx^2-1
={(cosecx)^2+ cosecx+(cosecx)^2-cosecx}/(cotx)^2
=2(cosecx)^2/(cotx)^2
=2(sinx)^2/(cosx)^2(sinx)^2
=2/(cosx)^2
=2(secx)^2=R.H.S.
hence proved
=(cosecx(cosecx+1)+ cosecx(cosecx-1))/cosecx^2-1
={(cosecx)^2+ cosecx+(cosecx)^2-cosecx}/(cotx)^2
=2(cosecx)^2/(cotx)^2
=2(sinx)^2/(cosx)^2(sinx)^2
=2/(cosx)^2
=2(secx)^2=R.H.S.
hence proved
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