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

Prove that cot^(-1)((pq+1)/(p-q))+cot^(-1)((qr+1)/(q-r)) +cot^(-1)((rp+1)/(r-p))=0 .

If p > q > 0a n dp r < -1 < q r , then find the value of tan^(-1)((p-q)/(1+p q))+tan^(-1)((q-r)/(1+q r))+tan^(-1)((r-p)/(1+r p)) .

If pgtqgt0 and prlt-1ltqr then prove that tan^(-1)((p-q)/(1+pq))+tan^(-1)((q-r)/(1+qr))+tan^(-1)((r-p)/(1+rp))=pi

If pgtqgt0 and prlt-1ltqr , then find the value of tan^(-1)((p-q)/(1+pq))+tan^(-1)((q-r)/(1+qr))+tan^(-1)((r-p)/(1+rp))

If pgtqgt0 and prlt-1ltqr , then find the value of tan^(-1)((p-q)/(1+pq))+tan^(-1)((q-r)/(1+qr))+tan^(-1)((r-p)/(1+rp))

Prove tan ^ (- 1) ((1) / (p + q)) + tan ^ (- 1) ((a) / (p ^ (2) + q + 1)) = cos ^ (- 1) p

show that: cot^(-1) ((pq + 1)/(p - q)) + cot^(-1) ((qr + 1)/(q - r)) + cot^(-1)((rp + 1)/(r - p)) = 0 .

If p>q>0 and pr<-1

Let theta=tan^(-1)((1)/(10))+tan^(-1)((1)/(9))+tan^(1)((1)/(8))+...+tan^(-1)(10)+tan^(-1)(11) and tan theta=(p)/(q) where p,q are coprime then p+q-6 is