Which of the following is/are true? `tan^-1|tan x|=|x|`

Which of the following is true? tan 1>tan^(-1)1

[ If xgt0 then which of the following is true 1) tan^(-1)xgt(x)/(1+x^(2)), 2) tan^(-1)x=(x)/(1+x^(2)) 3) tan^(-1)xlt(x)/(1+x^(2)), 4) tan^(-1)x!=(x)/(1+x^(2))]

Which of the following statements are true: (A) |tan^(-1)x-tan^(-1)y|<=|x-y|, where x,y are real numbers.

Let f(x)=cos^(-1)((1-tan^(2)(x)/(2))/(1+tan^(2)(x)/(2))) . Then which of the following statement is/are true ?

Let f(x)=cos^(-1)((1-tan^(2)(x)/(2))/(1+tan^(2)(x)/(2))) . Then which of the following statement is/are true ?

Let f(x)=cos^(-1)((1-tan^(2)(x)/(2))/(1+tan^(2)(x)/(2))) . Then which of the following statement is/are true ?

f(x)=tan x-tan^(3)+tan^(5)x-tan^(7)x+.........oo, then which of the following-is/are correct?

State which of the following is the value of tan""(1)/(3)( tan ^(-1) x + tan ^(-1)""(1)/(x))(x gt 0) ?

Which of the following inequalities are valid- |tan^(-1)x-tan^(-1)y|<=|x-y|AA x,y in R

If (tan^(-1)x)^(3)+(tan^(-1)y)^(3)=1-3tan^(-1)x.tan^(-1)y . Then which of the following may be true (a) (x+y)/(tan1)=-2 (b) (tan^(-1)x)/(1-tan^(-1)y)=2 (c) (tan^(-1)x)/(1-tan^(-1)y)=2 (d) (x+y)/(cot1)=1