Let `f : I - {-1,0,1} to [-pi, pi]` be defined as `f(x) = 2 tan^(-1) x - tan^(-1)((2x)/(1 -x^(2)))`, then which of the following statements (s) is (are) correct ?

Let f (x) =cos ^(-1) ((1-tan ^(2)(x//2))/(1+ tan ^(2) (x//2))) Which of the following statement (s) is/are correct about f (x) ?

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)=tan^(-1)((sqrt(1+x^(2))-1)/(x)) then which of the following is correct :

Let f(x)=sin(sin^(-1)2x)+cos ec(cos ec^(-1)2x)+tan(tan^(-1)2x) ,then which one of the following statements is/are incorrect?

Let f(x) = tan^(-1)(((x-2))/(x^(2)+2x+2)) ,then 26 f'(1) is

Find the range of f(x)= (1)/(pi)sin^(-1)x+tan^(-1)+(x+1)/(x^(2)+2x+5)

If f(x)=(sin^(-1)x+tan^(-1)x)/(pi)+2sqrt(x), then the range of f(x) is

Consider the following statements : 1. tan^(-1) x + tan^(-1)((1)/(x))=pi 2. There exist x, y in[-1, 1] , where x ne y such that sin^(-1) x + cos^(-1) y = (pi)/(2) . Which of the above statement is/are correct ?