Prove that
differentiating both sides of which we'll call (1), will give us: let's call this (2).
next in (1) change to to get: which with (1) gives us:
call this result (3). but we have the trig identity thus by (2) and (3) we have:
call this (4). finally equating the coefficients of in both sides of (4) gives us:
and the result follows.