Range of `tan^(-1)((2x)/(1+x^2))` is (a)`[-pi/4,pi/4]` (b) `(-pi/2,pi/2)` (c)`(-pi/2,pi/4)` (d) `[pi/4,pi/2]`

Range of function f(x)=cot^(-1)(2x-x^2), is (a) [pi/4,(3pi)/2] (b) [0,pi/4] [0,pi/2] (d) [pi/4,pi]

The range of f(x)=sin^(-1)((x^2+1)/(x^2+2)) is (a) [0,pi/2] (b) (0,pi/6) (c) [pi/6,pi/2] (d) none of these

The range of f(x)=sin^(-1)((x^2+1)/(x^2+2)) is (a)[0,pi/2] (b) (0,pi/6) (c) [pi/6,pi/2] (d) none of these

The function f(x)=tan^(-1)(sinx+cosx) is an increasing function in (-pi/2,pi/4) (b) (0,pi/2) (-pi/2,pi/2) (d) (pi/4,pi/2)

For 0 cos^(-1)(sintheta) is true when theta belongs to (a) (pi/4,pi) (b) (pi,(3pi)/2) (c) (pi/4,(3pi)/4) (d) ((3pi)/4,2pi)

Range of f(x)=sin^(-1)x+tan^(-1)x+sec^(-1)x is (a) (pi/4,(3pi)/4) (b) [pi/4,(3pi)/4] (c) {pi/4,(3pi)/4} (d) none of these

Prove that tan^-1((cosx)/(1+sinx))=pi/4-x/2,\ x in (-pi/2,pi/2)

The range of the function tan^(-1)((x^2+1)/(x^2+sqrt(3))),x in R is a. [pi/6,pi/2) b. [pi/6,pi/3) c. [pi/6,pi/4] d. none of these

The largest interval lying in (-pi/2,pi/2) for which the function [f(x)=4^-x^2+cos^(-1)(x/2-1)+log(cosx)] is defined, is (1) [0,pi] (2) (-pi/2,pi/2) (3) [-pi/4,pi/2) (4) [0,pi/2)

The largest interval lying in (-pi/2,pi/2) for which the function [f(x)=4^-x^2+cos^(-1)(x/2-1)+log(cosx)] is defined, is (1) [0,pi] (2) (-pi/2,pi/2) (3) [-pi/4,pi/2) (4) [0,pi/2)