Let `tan^(-1) y = tan^(-1) x + tan^(-1) ((2x)/(1 -x^(2))), " where " |x| lt (1)/(sqrt3)`. Then a value of y is

Let tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^2)) , where |x|<1/(sqrt(3)) . Then a value of y is : (1) (3x-x^3)/(1-3x^2) (2) (3x+x^3)/(1-3x^2) (3) (3x-x^3)/(1+3x^2) (4) (3x+x^3)/(1+3x^2)

y=tan^(-1)(x/(1+sqrt(1-x^2)))

y=tan^(-1)(x/(1+sqrt(1-x^2)))

y=tan^(-1)(x/(1+sqrt(1-x^2)))

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

If y = 2tan^(-1)x+sin^(-1)((2x)/(1+x^(2))) , then "………"lt y lt "………" .

tan^(-1)x-tan^(-1)y=tan^(-1)((x-y)/(1+xy)) holds good for

Prove that 3 tan^(-1) x= {(tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " -(1)/(sqrt3) lt x lt (1)/(sqrt3)),(pi + tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " x gt (1)/(sqrt3)),(-pi + tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " x lt - (1)/(sqrt3)):}

tan^(-1)""(x)/(sqrt(a^(2)-x^(2))),|x|lt a

Solve : tan^(-1)(x-1)+tan^(-1)x+tan^(-1)(x+1)=tan^(-1)3x