Prove that:`tan^(-1)((1-x^2)/(2x))+cot^(-1)((1-x^2)/(2x))=pi/2`

1.	Prove that:`tan^(-1)((1-x^2)/(2x))+cot^(-1)((1-x^2)/(2x))=pi/2`
Answer» `cot^-1 (1/x) = tan^-1 x` `tan^-1((1-x^2)/(2x)) + tan^-1((2x)/(1-x^2))` as we know `tan^-1 x + tan^-1 y = tan^-1((x+y)/(1-xy))` so, `tan^-1(((1-x^2)/(2x) + (2x)/(1-x^2))/(1- (1-x^3)/(2x)xx(2x)/(1-x^2)))` `= tan^-1(oo) = pi/2` hence proved

Discussion

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