trigonometry - Trigonometric Identities Like $A sin(x) + B cos(y) = cdots$

Are there any identities for trigonometric equations of the form:

$$A\sin(x) + B\sin(y) = \cdots$$
$$A\sin(x) + B\cos(y) = \cdots$$
$$A\cos(x) + B\cos(y) = \cdots$$

I can't find any mention of them anywhere, maybe there is a good reason why there aren't identities for these? Thanks!