prove that `tan^-1(cosx/(1-sinx))-cot^-1(sqrt(1+cosx)/sqrt(1-cosx))=pi/4 , xepsilon(0,pi/2)`

prove that `tan^-1(cosx/(1-sinx))-cot^-1(sqrt(1+cosx)/sqrt(1-cosx))=pi

1.	prove that `tan^-1(cosx/(1-sinx))-cot^-1(sqrt(1+cosx)/sqrt(1-cosx))=pi/4 , xepsilon(0,pi/2)`
Answer» `tan^(-1)A -tan^(-1)B=tan^(-1)((A-B)/(1+AB))`.......(1) Also `cot^(-1)x=tan^(-1)(1/x)` `tan^(-1)(cosx/(1-sinx))-tan^(-1)sqrt(((1-cosx)(1-cosx))/((1+cosx)(1-cosx))` `tan^(-1)(cosx/(1-sinx))-tan^(-1)((1-sinx)/cosx)` using (1) we get`tan^(-1)1=pi/4`

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