The range of the function `f(x)=int_(-1)^1(sinxdt)/((1-2tcosx+t^2)i s` (a)`[-pi/2,pi/2]` (b) `[0,pi]` (c)`{0,pi}` (d) `{-pi/2,pi/2}`

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)

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 value of the definite integral int_0^(pi/2)(sin5x)/(sinx)dxi s 0 (b) pi/2 (c) pi (d) 2pi

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

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

The range of f(x)=cos^(-1)((1+x^2)/(2x))+sqrt(2-x^2) is (a) {0,1+pi/2} (b) {0,1+pi) (c) {1,1+pi/2} (d) {1,1+pi}

int_(-(pi)/(2))^((pi)/(2))(sin^3xdx)/(1+cosx)= .

The range of f(x)=sec^(-1)((log)_3tanx+(log)_(tanx)3) is (a) [pi/3,pi/2)uu(pi/2,(2pi)/3] (b) [0,pi/2] (c) ((2pi)/3,pi) (d) none of these

Range of the function f(x)=sqrt(cos^(- 1)(sqrt(log_4x))-pi/2)+sin^(- 1)((1+x^2)/(4x)) is equal to (A) (0,pi/2+sqrt(pi/2)] (B) [pi/2,pi/2+sqrt(pi/2)] (C) [pi/6,pi/4) (D) {pi/6}