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]`

The range of f(x)=sin^(-1)(sqrt(x^(2)+x+1)) is (0,(pi)/(2))(b)(0,(pi)/(3))(c)((pi)/(3),(pi)/(2)) (d) [(pi)/(6),(pi)/(3)]

Prove that tan^(-1)((cos x)/(1+sin x))=(pi)/(4)-(x)/(2),|x in(-(pi)/(2),(pi)/(2))

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

The function f(x)=tan^(-1)(sin x+cos x) is an increasing function in (1)((pi)/(4),(pi)/(2))(2)(-(pi)/(2),(pi)/(4))(3)(0,(pi)/(2))(4)(-(pi)/(2),(pi)/(2))^(((pi)/(4)),(pi)/(2))^(((pi)/(4)))(2)

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

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

int_-1^1 sin^-1(x/(1+x^2))dx= (A) pi/4 (B) pi/2 (C) pi (D) 0

If y=tan^(-1)x+tan^(-1)(1/x)+sec^(-1)x , then y lies in the interval (a) [pi/2,pi)uu[pi,(3pi)/2) (b) [pi/2,(3pi)/2] (c)(0,pi) (d) [0,pi/2)uu[pi/2,pi)

The range of function f(x)=cot^(-1)x+sec^(-1)x+ cosec^(-1)x is (A) [(pi)/(2), pi)uu(pi, (3 pi)/(2)] (B) ((pi)/(2), (3 pi)/(4)] uu [(5 pi)/(4), (3 pi)/(2)) (C) ((pi)/(2), pi)uu(pi ,(3 pi)/(2)) (D) ((pi)/(2), (3 pi)/(2))