Prove that : `tan^(-1) x + cot^(-1) (1+x) = tan^(-1) (1+x+x^2)`

Prove that : (i) tan^(-1) x + cot^(-1)( x+1) = tan^(-1) (x^(2)+x+1) (ii) cot^(-1) 3 + "cosec"^(-1) sqrt(5) = pi/4

Prove that tan^(-1) x + cot^(-1) (x+1) = tan ^(-1) (x^(2) + x+1) .

Prove that : tan^(-1) x+cot^(-1) y = tan^(-1) ((xy+1)/(y-x))

prove that tan^(-1)x+cot^(-1)x=pi/2

Solve tan^(-1) x + cot^(-1) (-|x|) = 2 tan^(-1) 6x

Prove that : tan^(-1)x +tan^(-1). (2x)/(1-x^(2)) = tan^(-1) . (3x-x^(3))/(1-3x^(2)) , |x| lt 1/(sqrt(3))

Prove that tan(cot^(-1)x)=cot(tan^(-1)x)

Prove that : 2 tan^(-1) (cosec tan^(-1) x - tan cot^(-1) x) = tan^(-1) x

Prove that tan^(-1)(cot x)+cot^(-1)(tan x)=pi-2x

Prove that tan (2 tan^(-1) x ) = 2 tan (tan^(-1) x + tan^(-1) x^(3)) .