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

Prove that n.^(n-1)C_(r-1)=(n-r-1) ^nC_(r-1)

Prove that: ""^(n-1)P_r=(n-r)* ""^(n-1)P_(r-1)

Prove that cos[tan^(-1). {sin (cot^(-1)x)}]=sqrt((1+x^(2))/(2+x^(2))) .

Prove that: ((1+cot 60)/(1-cot 60))^2=(1+cos 30)/(1-cos 30)

Prove that .^(n-1)P_r+r.^(n-1)P_(r-1)=^nP_r .

Prove that .^(n+1)C_(r+1)+^nC_r+^nC_(r-1)=^(n+2)C_(r+1)

Prove that: ""^(n+1)P_(r+1)=(n+1)* ""^nP_r .

Prove that cot^(-1) ((sqrt(1+sin x) +sqrt(1-sin x))/(sqrt(1+sin x) -sqrt(1-sinx)))=(x)/(2), x in (0, (pi)/(4)) .

Prove the following: tan^-1x = cot^-1(frac{1}{x})