[sin[cot^(-1)(cos tan^(-1)x)]=],[[" A) "(x)/(sqrt(x^(2)+2))," B) "(x)/(sqrt(x^(2)+1))," C) "(1)/(sqrt(x^(2)+2))]" D) "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))

(d)/(dx)[cos^(-1)(x sqrt(x)-sqrt((1-x)(1-x^(2))))]=(1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))(-1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))(1)/(sqrt(1-x^(2)))+(1)/(2sqrt(x-x^(2)))(1)/(sqrt(1-x^(2)))0 b.1/4c.-1/4d none of these

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))

Differential coefficient of sec(tan^(-1)x) is (x)/(1+x^(2))( b) x sqrt(1+x^(2))(c)(1)/(sqrt(1+x^(2))) (d) (x)/(sqrt(1+x^(2)))

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

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

(tan^(-1)x)/(sqrt(1-x^(2))) withrespectto sin ^(-1)(2x sqrt(1-x^(2)))

tan^(-1)[(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2)))]=(pi)/(4)+(1)/(2)cos^(-1)x^(2)

IfI=int(dx)/(x^(3)sqrt(x^(2)-1)), then Iequals a.(1)/(2)((sqrt(x^(2)-1))/(x^(3))+tan^(-1)sqrt(x^(2)-1))+C b.(1)/(2)((sqrt(x^(2)-1))/(x^(2))+x tan^(-1)sqrt(x^(2)-1))+Cc(1)/(2)((sqrt(x^(2)-1))/(x^(2))+tan^(-1)sqrt(x^(2)-1))+Cd(1)/(2)((sqrt(x^(2)-1))/(x^(2))+tan^(-1)sqrt(x^(2)-1))+C

tan(cos^(-1)x) is equal to (x)/(1+x^(2)) b.(sqrt(1+x^(2)))/(x) c.(sqrt(1-x^(2)))/(x) d.sqrt(1-2x)