Question

Prove that:

tan^-1x + cot^-1 (x + 1) = tan^-1 (x² + x + 1)

Answer 1

To Prove: 

tan ^-1 x + cot ^-1 (x + 1) = tan ^-1 (x ² + x + 1) 

Formula Used:

Proof: 

LHS = tan ^-1 x + cot ^-1 (x + 1) … (1)

= tan ^-1 (x ² + x + 1) 

= RHS 

Therefore, LHS = RHS 

Hence proved.