If `p+q+r=0` then show that `1/(1+x^p+x^(-q)) + 1/(1+x^q+x^(-r)) + 1/(1+x^r+x^(-p)) =1`

If y = (1)/(1+x^( p-r) +x^(q-r)) +(1)/( 1+ x^(p-q) +x^(r-q) )+ (1) /( 1+x^(q-p) +x^(r-p)),then (dy)/(dx) =

x^(p-q).x^(q-r).x^(r-p)

sqrt(x^(p-q))sqrt(x^(q-r))sqrt(x^(r-p))=1

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

If 5^(-p)=4^(-q)=20^(r) show that (1)/(p)+(1)/(q)+(1)/(r)=0