Is there a trigonometric identity for $\sin(ab)$? Thanks in advance! I can't find it anywhere. Bothering me a lot.
For that matter, what about $\sin(a^{-1})$?
Both of these for cosine, too, but if you can get any one of these 4, that would be great.
This might help get the creative juices flowing!
I don't know the answer, and this isn't really a complete answer, it is more of a comment:
Perhaps use the fact that $sin(ab)$ is the imaginary part of $e^{iab}=(e^{ia})^b = (\cos a + i \sin a)^b$, and then use some binomial expansion formula. For example, taking $b=2$ recovers $\sin(2a)=2\cos(a)\sin(a)$, and similar expressions for other positive integers $b$ (I think chebyshev polynomials arise). Of course, $b$ need not be an integer, but there is still a binomial expansion for real numbers $b$, and maybe something can still be said, I don't know.