If `sin^(-1)(x-1)+cos^(-1)(x-3)+tan^(-1)(x/(2-x^2))=cos^(-1)k+pi,` then the value of `k` is (a)1 (b) `-1/(sqrt(2))` (c) `1/(sqrt(2))` (d) non of these

If 4\ cos^(-1)x+sin^(-1)x=pi , then the value of x is (a) 3/2 (b) 1/(sqrt(2)) (c) (sqrt(3))/2 (d) 2/(sqrt(3))

If 3\ sin^(-1)((2x)/(1+x^2))-4\ cos^(-1)((1-x^2)/(1+x^2))+2\ tan^(-1)((2x)/(1-x^2))=pi/3 , then x is equal to 1/(sqrt(3)) (b) -1/(sqrt(3)) (c) sqrt(3) (d) -(sqrt(3))/4

If 3\ sin^(-1)((2x)/(1+x^2))-4\ cos^(-1)((1-x^2)/(1+x^2))+2\ tan^(-1)((2x)/(1-x^2))=pi/3 , then x is equal to (a) 1/(sqrt(3)) (b) -1/(sqrt(3)) (c) sqrt(3) (d) -(sqrt(3))/4

If 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-2)((2x)/(1-x^2))=pi/3, w h e r e|x|<1, then x is equal to 1/(sqrt(3)) (b) -1/(sqrt(3)) (c) sqrt(3) (d) -(sqrt(3))/4

The value of (lim)x->0(sqrt(1-cos"x"^2))/(1-cosx) is a. 1/2 b. 2 c. sqrt(2) d. none of these

If |cos^(-1)((1-x^2)/(1+x^2))| < pi/3,t h e n (a) x in [-1/3,1/(sqrt(3))] (b) x in [-1/(sqrt(3)),1/(sqrt(3))] x in [0,1/(sqrt(3))] (d) none of these

If sin^(-1)x-cos^(-1)x=pi/6 , then x= (a) 1/2 (b) (sqrt(3))/2 (c) -1/2 (d) none of these

If int( 2^(x))/( sqrt( 1- 4^(x))) dx = k sin^(-1) ( 2^(x)) + C , then the value of k is

If int cos^(-1)x+cos^(-1)sqrt(1-x^2) dx= Ax+f(x)sin^(-1)x-2sqrt(1-x^2)+c then

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)