Question

If tanx+tany=q , cotx+coty =p and x+y=c then prove that (p-q)tanc =pq

Answer 1

(p-q)tanc =(p-q)tan(x+y)= (p-q) $\frac{ tanx+tany}{1-tanx \cdot tany}$ =(p-q) $\frac{ q}{1-\frac {tanx + tany}{cotx+coty}}$ =(p-q)$\frac{q}{1-\frac{q}{p}}$ =(p-q) $\frac{q}{\frac{p-q}{p}}$ =(p-q)$\frac{pq}{p-q}$ =pq