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" AMPLE "9" Prove that: "tan^(-1)(1-x)/(...

" AMPLE "9" Prove that: "tan^(-1)(1-x)/(1+x)-tan^(-1)(1-y)/(1+y)=sin^(-1)(y-x)/(sqrt(1+x^(2))sqrt(1+y^(2)))

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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)/(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)/(sqrt((1+x^2)(1+y^2))))

tan ^(-1)""(1-x)/(1+x)- tan ^(-1 )""(1-y)/(1+y) = sin ^(-1) ""(y-x)/(sqrt((1+x^(2))(1+y^(2)))

Prove the following "tan"^(-1)((1-x)/(1+x))-"tan"^(-1)((1-y)/(1+y))="sin"^(-1)((y-x)/(sqrt(1+x^(2))sqrt(1+y^(2)))) .

y=tan^(-1)((x)/(1+sqrt(1-x^(2))))

y=tan^(-1)(x/(1+sqrt(1-x^2)))

y=tan^(-1)(x/(1+sqrt(1-x^2)))

y=tan^(-1)(x/(1+sqrt(1-x^2)))

y=tan^(-1)(x/(1+sqrt(1-x^2)))