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

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]

Let f(x)=sin^(-1)x+|sin^(-1)x|+sin^(-1)|x| The range of f(x) is (a) [0,(pi)/(2)] (b) [0,(3pi)/(2)] (c) [0,(pi)/(4)] (d) [0,pi]

The set of all x in ((-pi)/2,pi/2) satisfying |4sinx-1| (a) (-pi/(10),(3pi)/(10)) (b) (pi/(10),(3pi)/(10)) (c) (pi/(10),(3pi)/(10)) (d) none of these

tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y)) is (A) pi/2 (B) pi/3 (C) pi/4 (D) pi/4 or (3pi)/4

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)=|6sin^(-1)x-pi|+|6cos^(-1)x-pi| is (a) [0,9pi] (b) [0,3pi] (c) [pi,3pi] (d) [ pi,9pi]

tan^(-1)(x/y)-tan^(-1)(x-y)/(x+y) is equal to(A) pi/2 (B) pi/3 (C) pi/4 (D) (-3pi)/4

tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y)) is equal to (A) pi/2 (B) pi/3 (C) pi/4 (D) (-3pi)/4

The principal value of sin^(-1)(sin((2pi)/3)) is (a) -(2pi)/3 (b) (2pi)/3 (c) (4pi)/3 (d) (5pi)/3 (e) none of these

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)