You need to use Trigonometric Identities...
Now let and the equation becomes
which is a quadratic equation that you can solve for , the solution of which you can use to solve for .
if I have p/k=sin(3x)/sin(2x), how could I solve for x in terms of p/k? I understand that these are not linear functions so they cannot be solved simultaneously but is it possible to approximately solve this problem using taylor expansions? If there is another way I could solve this, I would like to hear what you think. Thank you