[" 9.Prove that "],[qquad [sqrt(1+x^(2)),+cos^(-1)(x+1)/(sqrt(x^(2)+2x+2))],[=,tan^(-1)(x^(2)+x+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)

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

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

Prove that tan^(-1)[(sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))]=pi/4+1/2cos^(-1)x^2

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

Prove that cos[tan^(-1). {sin (cot^(-1)x)}]=sqrt((1+x^(2))/(2+x^(2))) .

prove that tan^(-1) sqrt x = 1/2 cos^(-1)((1-x)/(1+x)), x in [0,1]

Prove that tan^(-1) sqrt(x) =(1)/(2) cos^(-1) ((1-x)/(1+x)) , x in [0, 1]

Prove that tan^(-1)backslash(sqrt(1+x^(2))-1)/(x)=(1)/(2)tan^(-1)x

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