Is it possible to rearrange $\tan(y) = \frac{\sin(x)}{\cos(x)+C}$ for x, where C is a constant?
Thank you for any suggestions!
2026-03-26 14:42:09.1774536129
Is it possible to rearrange this for x?
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$$\tan(y) = \frac{\sin(x)}{\cos(x)+C} \\ \implies \frac{\sin(y)}{\cos(y)}=\frac{\sin(x)}{\cos(x)+C} \\ \implies \sin(y)(\cos(x)+C) = \sin(x)\cos(y) \\ \implies \sin(y)\cos(x)+C\sin(y) = \sin(x)\cos(y) \\ \implies \sin(y)\cos(x)-\sin(x)\cos(y)=-C\sin(y) \\ \implies \sin(y-x)=-C\sin(y) \\ \implies y-x = \arcsin\left[-C\sin(y) \right] \\ \implies x = y-\arcsin\left[-C\sin(y) \right]$$