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

Prove that i) cos^(-1)(1-2x^(2))=2sin^(-1)x ii) cos^(-1)(2x^(2)-1)=2cos^(-1)x . iii) sec^(-1)(1/(2x^(2)-1)=2cos^(-1)x iv) cot^(-1)(sqrt(1-x^(2))-x)=pi/2-1/2cot^(-1)x .

Prove the followings : cot^(-1)((sqrt(1+x^(2))-1)/x)=pi/2-1/2tan^(-1)x

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

The solution set of inequality (cot^(-1)x)(tan^(-1)x)+(2-(pi)/(2))cot^(-1)x-3tan^(-1)x-3(2-(pi)/(2))>0 is (a,b), then the value of cot ^(-1)a+cot^(-1)b is

cot ^(-1)""x+cot^(-1)""2x=(3pi)/(4)

3cot^(-1)((1)/(2-sqrt(3)))+cot^(-1)x=(pi)/(2)

Show that int_(0)^(pi)cos (2 cot^(-1) (sqrt((1-x)/(1+x))))dx = -(1)/(2)

(d)/(dx)[cot^-1((1+sqrt(1-x^(2)))/(x))]=