You probably meant to say "how to solve" instead "how to prove," since as it's written, it just holds for certain values, in fact, it's a trig. equation.
cannot be proved because it is not true. I think that what you meant to ask is how to solve that equation for
Try squaring both sides and expanding:
Letting , you have
Solve for y by inspection. I see one obvious value of y such that
Then find when equals that value of y and you're done.
Note: there is more than one solution. In fact, there are infinitely many solutions to this problem because sine is a periodic function.