`y=tan^(-1)(x/(1+sqrt(1-x^2)))`

Differentiate tan^(-1)(x/(1+sqrt((1-x^2)))) +{2tan^(-1)sqrt(((1-x)/(1+x)))}sinwdotrdottdotxdot

If -1< x < 0 , then cos^(-1)x is equal to (a) sec^(-1)(1/ x) (b) pi-sin^(-1)sqrt(1+x^2) (c) pi+tan^(-1)(x/(sqrt(1-x^2))) (d) cot^(-1)(x/(sqrt(1-x^2))) .

"F i n d"(dy)/(dx)"if"y=tan^(-1)((sqrt(1+x^2)-1)/x), where x!=0

Which of the following pairs of function/functions has same graph? y=tan(cos^(-1)x); y=(sqrt(1-x^2))/x y=t a n(cot^(-1)x);y=1/x y="sin"(tan^(-1)x); y=x/(sqrt(1-x^2)) y="cos"(tan^(-1)x); y=s in(cot^(-1)x)

If y = (sin^(-1) x)/(sqrt(1-x^2)) show that (1-x^2) y_2 - 3xy_1 - y =0

y=tan^(-1)((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))),w h e r e -1

Prove that tan^(-1)((1-x)/(1+x))-tan^(-1)((1-y)/(1+y))=sin^(-1)((y-x)/(sqrt(1+x^(2))*sqrt(1+y^(2))))