Rewriting $\sin(a+b) = c$ Given $$\sin(a+b) = c$$
Could it be rewritten as $$a = \arcsin(c) - b$$
For all reals $a$ and $b$?
Sine over reals isn't one-to-one though. Is the above valid?

This formula doesn't work for all real numbers since the range of $\arcsin(x)$ is $[-\frac{\pi}{2}, \frac{\pi}{2}]$. For example, $$\sin (\frac{3\pi}{2} + \frac{\pi}{4}) = -\frac{\sqrt 2}{2}$$ but $$\arcsin\left(-\frac{\sqrt 2}{2}\right) - \frac{\pi}{4} = -\frac{\pi}{2} \neq \frac{3\pi}{4}.$$
