Prove `tan^(-1)(1/(p+q))+tan^(-1)(q/(p^2+pq+1))=cot^(-1)p`

1.	Prove `tan^(-1)(1/(p+q))+tan^(-1)(q/(p^2+pq+1))=cot^(-1)p`
Answer» LHS `tan^(-1)(1/(p+q))+tan^(-1)(q/(p^2+pq+1))` `tan^(-1)(((1/(p+q))+(q/(p^2+pq+1)))/(1-(1/(p+q))*(q/(p^2+pq+1))))` `tan^(-1)(((p+q)^2+1)/(p((p+q)^2+1)))` `tan^(-1)(1/p)` `cot^(-1)(p)` RHS.

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Prove `tan^(-1)(1/(p+q))+tan^(-1)(q/(p^2+pq+1))=cot^(-1)p`

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