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

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

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

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

If x lt 0 , the prove that cos^(-1) ((1 + x)/(sqrt(2(1 + x^(2))))) = (pi)/(4) - tan^(-1) x

tan^(- 1)(1/(sqrt(x^2-1))),|x|gt1

Differentiate tan^(-1)((x)/(sqrt(1-x^(2)))) with respect to cos^(-1)(2x^(2)-1) .

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

Differentiate tan^(-1) ((sqrt(1+x^(2))-1)/(x)) w.r.t. tan^(-1) ((x)/(sqrt(1-x^(2)))) .

tan^-1 [(1)/(sqrt(x^2-1))]

Statement -1: if -1lexle1 then sin^(-1)(-x)=-sin^(-1)x and cos^(-1)(-x)=pi-cos^(-1)x Statement-2: If -1lexlex then cos^(-1)x=2sin^(-1)sqrt((1-x)/(2))= 2cos^(-1)sqrt((1+x)/(2))