If `(1-tanx)/(1+tanx)=tany` and `x-y = pi/6`, then `x,y` are respectively (A) `(5pi)/24,pi/24` (B) `-(7pi)/24, - (11pi)/24` (C) `-(115pi)/24, (-119pi)/24` (D) none of these

(1-tanx)/(1+tanx)=tanyandx-y=pi/6,t h e nx , y

sin^-1 (sin ((7pi)/6))= (A) (7pi)/6 (B) pi/6 (C) -pi/6 (D) none of these

int_-pi^(3pi) cot^-1(cotx)dx= (A) pi^2 (B) 2pi^2 (C) 3pi^2 (D) none of these

If f(x)=sin^(-1)cosx , then the value of f(10)+f^(prime)(10) is (a) 11-(pi)/2 (b) (pi)/2-11 (c) (5pi)/2-11 (d) none of these

If tan(A-B)=1,sec(A+B)=2/(sqrt(3)) , then the smallest positive value of B is. (a) (25pi)/(24) (b) (19pi)/(24) (c) (13pi)/(24) (d) (11pi)/(24)

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

If tan(A-B)=1a n dsec(A+B)=2/(sqrt(3)) , then the smallest positive values of A and B, respectively, are (25pi)/(24),(19pi)/(24) (b) (19pi)/(24),(25pi)/(24) (31pi)/(24),(31pi)/(24) (d) (13pi)/(24),(31pi)/(24)

sin^-1 (-1/2)+tan^-1 (sqrt(3))= (A) -pi/6 (B) pi/3 (C) pi/6 (D) none of these

int_0^oo(x dx)/((1+x)(1+x^2)) is equal to (A) pi/4 (B) pi/2 (C) pi (D) none of these"

The value of sin^(-1)(-sqrt3/2)+cos^(-1)(cos\ (7pi)/6) is a. (5pi)/6 b. pi/2 c. (3pi)/2 d. none of these