`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`

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

If alpha=tan^(-1)((sqrt(3)x)/(2y-x)) , beta=tan^(-1)((2x-y)/(sqrt(3)y)) , then alpha-beta= (a) pi/6 (b) pi/3 (c) pi/2 (d) -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

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]

Let f(x)=tan^(-1)(1/2 tan2x)+tan^(-1)(cotx)+tan^(-1)(cot^3x) then (1) f((3 pi)/8)=pi (2) f(pi/8)=0 (3) f(pi/8) =pi (4) f((3pi)/8)=0

If y="sec"(tan^(-1)x),t h e n (dy)/(dx) at x=1 is (a) cos(pi/4) (b) sin(pi/2) (c) sin(pi/6) (d) cos(pi/3)

The value of tan^(-1)(1)+cos^(-1)(-1/2)+sin^(-1)(-1/2) is equal to pi/4 b. (5pi)/(12) c. (3pi)/4 d. (13pi)/(12)

If x >1 , then 2\ tan^(-1)x+sin^(-1)((2x)/(1+x^2)) is equal to (a) 4tan^(-1)x (b) 0 (c) pi/2 (d) pi

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]