To Prove: tan^-1 x + cot^-1 (x + 1) = tan^-1 (x² + x + 1)

Formula Used:

1)

2)

Proof:

LHS = tan^-1 x + cot^-1 (x + 1) … (1)

= tan^-1 (x² + x + 1)

= RHS

Therefore, LHS = RHS

Hence proved.