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

If (x -1) (x^(2) + 1) gt 0 , then find the value of sin((1)/(2) tan^(-1)((2x)/(1 - x^(2))) - tan^(-1) 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

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^(2) + 1) gt 0 , then find the value of sin((1)/(2) tan^(-1).(2x)/(1 - x^(2)) - tan^(-1) x)

If (x -1) (x^(2) + 1) gt 0 , then find the value of sin((1)/(2) tan^(-1).(2x)/(1 - x^(2)) - tan^(-1) x)

If (x -1) (x^(2) + 1) gt 0 , then find the value of sin((1)/(2) tan^(-1).(2x)/(1 - x^(2)) - tan^(-1) x)

If (x -1) (x^(2) + 1) gt 0 , then find the value of sin((1)/(2) tan^(-1).(2x)/(1 - x^(2)) - tan^(-1) x)