If `sin^(-1)((4x)/(x^2+4))+2tan^(-1)(-x/2)` is independent of `x ,` find the values of `xdot`

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 sin^(-1) ((4x)/(x^(2)+4)) + 2 tan^(-1)( - x/2) is independent of x , then

If x+1/x=12 , find the value of x-1/xdot

If 2tan^(-1)x+sin^(-1)((2x)/(1+x^2) ) is independent of x then :

If tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/(x+2))=pi/4 , then find the value of x .

If tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/(x+2))=pi/4, then find the value of xdot

If sin^(-1)(2x)/(1+x^2)=tan^(-1)(2x)/(1-x^2) , then find the value of xdot

If cos(2sin^(-1)x)=1/9, then find the values of xdot

If cos^(-1)((6x)/(1+9x^2))=-pi/2+2tan^(-1)3x , then find the value of xdot

If tan^(-1)x-cot^(-1)x=tan^(-1)""1/(sqrt(3)) find the value of xdot

tan^-1 (x-1)/(x-2) + tan^-1 (x+1)/(x+2)=pi/4. find X