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!

$A \, \cos(x) + B \, \cos(y)= C \, \cos(z)$, where,
$$ C = \sqrt{(A \, \cos(x) + B \, \cos(y))^2 + (A \, \sin(x) + B \, \sin(y))^2}, $$
and
$$ z = \tan^{-1}\left(\frac{A \, \sin(x) + B \, \sin(y)}{A \, \cos(x) + B \, \cos(y)}\right). $$
