The value of `sin(cot^-1x)=` (A) `sqrt(1+x^2)` (B) x (C) `(1+x^2)^(-3/2)` (D) `(1+x^2)^(-1/2)`

Solve the equations. sin(tan^(-1)x),|x|<1 (A) x/(sqrt(1-x^2)) (B) 1/(sqrt(1-x^2)) (C) 1/(sqrt(1+x^2)) (D) x/(sqrt(1+x^2))

The value of tan{1/2 sin^-1 ((2x)/(1+x^2))+1/2 cos^-1 ((1-x^2)/(1+x^2))} is (A) (2x)/(1-x^2) (B) (2x)/(1-x^2) (C) not defined if x.>=1 (D) 0

The value of lim_(x->1)(1-sqrt(x))/((cos^(-1)x)^2) is 4 (b) 1/2 (c) 2 (d) 1/4

int(x^3dx)/(sqrt(1+x^2)) is equal to (A) 1/3sqrt(1+x^2)(2+x^2)+C (B) 1/3sqrt(1+x^2)(x^2-1)+C (C) 1/3(1+x^2)^(3/2)+C (D) 1/3sqrt(1+x^2)(x^2-2)+C

the value of cos(cos^-1x+sin^-1(x-2)) is equal to (A) 0 (B) 1 (C) -1 (D) sqrt(1-x^2).sqrt(x^2-4x+3) +x (x-2)

The solution set of equation sin^(-1) sqrt(1-x^2) + cos^(-1) x = cot^(-1) (sqrt(1 - x^2)/x) - sin^(-1) x , is

The value of int(a x^2-b)/(xsqrt(c^2x^2-(a x^2+b)^2)) (a) 1/csin^(-1)(a x+b/x)+k (b) csin^(-1)(a+b/x)+e (c) sin^(-1)((a x+b/x)/c)+k (d) none of these

Prove that cos (tan^(-1) (sin (cot^(-1) x))) = sqrt((x^(2) + 1)/(x^(2) + 2))

The value of x=sqrt(2+sqrt(2+sqrt(2+...))) is (a) -1 (b) 1 (c) 2 (d) 3

The value of x for which "sin"(cot^(-1)(1+x))="cos"(tan^(-1)x) is 1/2 (b) 1 (c) 0 (d) -1/2