If `x >1` , then `2\ tan^(-1)x+sin^(-1)((2x)/(1+x^2))` is equal to `4tan^(-1)x` (b) 0 (c) `pi/2` (d) `pi`

If x >1 , then 2\ tan^(-1)x+sin^(-1)((2x)/(1+x^2)) is equal to (a) 4tan^(-1)x (b) 0 (c) pi/2 (d) pi

int_(0) ^(pi//2) (dx)/( 1 + tan^(3) x) is equal to a)1 b) pi c) pi/2 d) pi/4

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

If tan^(-1)(a//x)+tan^(-1)(b//x)=pi//2 then x=

tan^(-1)((a)/(x))+tan^(-1)((b)/(x))=(pi)/(2) then x=