If `x gt 1` then `2tan^(-1)x - tan^(-1) ((2x)/(1-x^(2)))` =______.

2tan^(-1)x = tan^(-1) 2x/(1-x^(2)) is true if

If x gt 1 then 1/2 cos^(-1) ((x^(2)-1) /(x^(2)+1)) = tan^(-1) _______.

If x gt (1)/sqrt(3) then tan^(-1) (3x-x^(3))/(1-3x^(2)) equals

sec^(-1)((1+tan^(2)x)/(1-tan^(2)x))

sin^(-1)((1-tan^(2)x)/(1+tan^(2)x))

Given that , tan^(-1) ((2x)/(1-x^(2))) = {{:(2 tan^(-1) x"," |x| le 1),(-pi +2 tan^(-1)x","x gt 1),(pi+2 tan^(-1)x"," x lt -1):} sin^(-1)((2x)/(1+x^(2))) ={{:(2 tan^(-1)x","|x|le1),(pi -2 tan^(-1)x","x gt 1 and ),(-(pi+2tan^(-1))","x lt -1):} sin^(-1) x + cos^(-1) x = pi//2 " for " - 1 le x le 1 If cos^(-1). (6x)/(1 + 9x^(2)) = - pi/2 + 2 tan^(-1) 3x" , then " x in

Prove that tan^(-1)(x+1)+tan^(-1)(x-1)=tan^(-1)((2x)/(2-x^2))