" (武户) "cot^(-1)((1)/(sqrt(x^(2)-1))),x<-1

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

Show that cot^(-1)((1)/(sqrt(x^(2)-1)))=sec^(-1)x,|x|gt1 .

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

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

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

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