Question 835917
If 
(1) {{{p*tan(x) = tan(px)}}}
Then what is
(2) {{{p*sin^2(x)/sin^2(px)}}}
Solve (1) for p to get
(3) {{{p = tan(px)/tan(x)}}}
Now put p of (3) into (2) and get
(4) {{{(tan(px)/tan(x))*(sin^2(x)/sin^2(px))}}} or
(5) {{{(sin^2(x)/tan(x))*(tan(px)/sin^2(px))}}} 
Now use the identity
(6) {{{tan(x) = sin(x)/cos(x)}}}
to get
(7) {{{(sin(x)*cos(x))*(1/(cos(px)*sin(px)))}}} 
Now use the identity
(8) {{{sin(x)*cos(x) = sin(2*x)/2}}}
to get
(8) {{{(sin(2*x)/sin(2*px)))}}} 
Answer: {{{p*sin^2(x)/sin^2(px) = sin(2*x)/sin(2*px)}}}