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 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}

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))i s (0,pi/2) (b) (0,pi/3) (c) [pi/3,pi/2] (d) [pi/6,pi/3]

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

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

The value of c in Lagranges theorem for the function f(x)=logsinx in the interval [pi/6,(5pi)/6] is (a) pi/4 (b) pi/2 (c) (2pi)/3 (d) none of these

find the range of function f(x)=sin(x+(pi)/(6))+cos(x-(pi)/(6))

The least and the greatest values of (sin^(-1)x)^3+(cos^(-1)x)^3 are (a) (-pi)/2,pi/2 (b) (-pi^3)/8,(pi^3)/8 (c) (pi^3)/(32),(7pi^3)/8 (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}