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)`

The value of cos [ tan^-1 {sin (cot^-1 (x))}] is a) sqrt((x^2+1)/(x^2-1)) b) sqrt((1-x^2)/(x^2+2)) c) sqrt((1-x^2)/(1+x^2)) d) sqrt((x^2+1)/(x^2+2))

The value of cot(tan^(-1)2x+cot^(-1)2x) is ... (A) 0 (B) 2x (C) 4x (D) pi+2x A B C D

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

d/(dx)(sin^(-1)x+cos^(-1)x) is equal to : (A) (1)/(sqrt(1-x^(2))), (B) (2)/(sqrt(1-x^(2))), (C) 0 (D) sqrt(1-x^(2))

The minimum values of sin x + cos x is a) sqrt2 b) -sqrt2 c) (1)/(sqrt2) d) - (1)/(sqrt2)

If x = sqrt7 + sqrt6 , then find the simpliest value of (a) x - (1)/(x) , (b) x + (1)/(x) , (c) x^(2) + (1)/(x^(2)) , (d) x^(3) + (1)/(x^(3))

If x takes negative permissible values , then sin^(-1) x= a) cos^(-1)sqrt(1-x^2) b) -cos^(-1)sqrt(1-x^2) c) cos^(-1)sqrt(x^2-1) d) pi-cos^(-1)sqrt(1-x^2)

int sqrt((1-x)/(1+x))dx is equal to a) sin^(-1)x + sqrt(1 - x^(2)) + C b) sin^(-1) x - 2 sqrt(1 - x^(2)) + C c) 2 sin^(-1) x - sqrt(1 - x^(2)) + C d) sin^(-1)x - sqrt(1 - x^(2)) + C

Choose the correct answer int sqrt(1+x^2) d x is equal to A) x/2 sqrt(1+x^2)+1/2 log |x+sqrt(1+x^2)|+C B) 2/3(1+x^2)^(3 / 2)+C C) 3/2 x(1+x^2)^(3 / 2)+C D) x^2/2 sqrt(1+x^2)+1/2 x^2 log |x+sqrt(1+x^2)|+C

If x<0,t h e ntan^(-1)x is equal to -pi+cot^(-1)1/x (b) sin^(-1)x/(sqrt(1+x^2)) -cos^(-1)1/(sqrt(1+x^2)) (d) -cos e c^(-1)(sqrt(1+x^2))/x