" 2.(i) "sqrt(cot^(-1)sqrt(x))

" 2.(i) sqrt(3x+1)-sqrt(x-1)=2

cot^(-1)((1)/(sqrt(x)))

Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1)x/(sqrt(1-x^(2))) (iii) "cot"^(-1)(sqrt(1-x^(2)))/x

Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1)x/(sqrt(1-x^(2))) (iii) "cot"^(-1)(sqrt(1-x^(2)))/x

cot^(-1)(sqrt(1+x^2)-x)

Evaluate each of the following: (i) cot^(-1)(1/(sqrt(3)))-"cosec"^(-1)(-2)+sec^(-1)(2/(sqrt(3))) (ii) cot^(-1){2cos(sin^(-1)((sqrt(3))/2))}

If I=underset (0)overset(1) int cos{ 2 "cot"^(-1)sqrt((1-x)/(1+x))}dx then

If I=int_(0)^(1) cos{ 2 "cot"^(-1)sqrt((1-x)/(1+x))}dx then

Differentiate the following functions with respect to x : (i) tan^(-1){(sqrt(1+x^2)+1)/x},\ \ x!=0 (ii) cot^(-1){sqrt(1+x^2)+x}