Prove that:`tan^(-1)((1-x)/(1+x))-tan^(-1)((1-y)/(1+y))=sin^(-1)((y-x)/(sqrt((1+x^2) (1+y^2))))`

Prove that:`tan^(-1)((1-x)/(1+x))-tan^(-1)((1-y)/(1+y))=sin^(-1)((y-x)

1.	Prove that:`tan^(-1)((1-x)/(1+x))-tan^(-1)((1-y)/(1+y))=sin^(-1)((y-x)/(sqrt((1+x^2) (1+y^2))))`
Answer» `tan^-1( (1-x)/(1+x)) - tan^-1 ((1-y)/(1+y))` `tan^-1 (1) - tan^-1 x - [tan^-1 (1) - tan^-1 y]` `= tan^-1 y - tan^-1 x` `= tan^-1 ((y-x)/(1+xy))` `= sqrt(y^2 +x^2 -2xy+1+ x^2y^2 + 2xy)` `= sqrt(y^2(1+x^2)+1(1+x^2))` `= sqrt((y^2+1)(1+x^2)` `sin^-1 ((y-x)/(sqrt(1+x^2)sqrt(1+y^2)))` answer

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