Very simple question regarding sum/difference identity

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If I have $\sin(0.7x-47t+C)$ where do I carry my constant $C$? The same with my sum-to-product identities.

This problem is showing up for me because I'm studying mechanical waves at the moment.

I thank you in advance.

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Hint: $\sin{(A+C-B)}=\sin{(A)}\cos{(C-B)}+\cos{(A)}\sin{(C-B)}$

Can you use the angle difference identities for sine and cosine from here?