Can you please tell me if such an identity exists

Question

Which trigonometric identity is this

$$ A\sin(wt)+B\sin(wt+s)=A\sin(wt)+B \sin(wt)\cos(s)+B\cos(wt)\sin(s) $$

Answer 1

$A\sin(wt)+B\sin(wt+s)=A\sin(wt)+B\sin(wt)\cos(s)+B\cos(wt)\sin(s)$

$A\sin(wt)$ cancels out on both sides, giving us $$B\sin(wt+s)=B\sin(wt)\cos(s)+B\cos(wt)\sin(s)$$ We then divide both sides by $B$, $$\sin(wt+s)=\sin(wt)\cos(s)+\cos(wt)\sin(s)$$

Which is the trigonometric identity: $$\sin(x+y) = \sin(x)\cos(y) + \cos(x)\sin(y)$$

Answer 2

Apply the rule: $\sin(x+y) = \sin(x)\cos(y) + \cos(x)\sin(y)$