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

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

If f(x)=sin^(-1)cos x, then the value of f(10)+f'(10) is (a)11-(7 pi)/(2) (b) (7 pi)/(2)-11 (c) (5 pi)/(2)-11( d) none of these

If y=[(tanx)^(tanx)]^(tanx) ,then at x=pi/4 , the value of (dy)/(dx)=

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

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

int_0^21/(1+tanx)dx is equal to (pi^)/4 (b) (pi^)/3 (c) (pi^)/2 (d) pi

If sin^(-1)x+sin^(-1)y=(2 pi)/(3) ,then the value of cos^(-1)x+cos^(-1)y is (A) (2 pi)/(3) (B) (pi)/(3) (C) (pi)/(2) (D) pi

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

If y=tan^(-1)x+tan^(-1)(1/x)+sec^(-1)x , then y lies in the interval (a) [pi/2,pi)uu[pi,(3pi)/2) (b) [pi/2,(3pi)/2] (c)(0,pi) (d) [0,pi/2)uu[pi/2,pi)

If f(x)=tanx and A,B,C are the anlges of /_\ABC, then |(f(A), f(pi/4) f(pi/4)), (f(pi/4), f(B) f(pi/4)), (f(pi/4), f(pi/4) f(C))|= (A) 0 (B) -2 (C) 2 (D) 1