identify incorrect law of sines equation

1. Understand the Law of Sines: The Law of Sines states that for any triangle $ABC$ with sides $a, b, c$ opposite to angles $A, B, C$ respectively, the ratio of a side length to the sine of its opposite angle is constant: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ This can also be written as the reciprocal: $$\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$$

2. Analyze the given options: We need to check which equation does not follow the correct pairing of side and opposite angle.
- Option A: $\frac{c}{\sin C} = \frac{a}{\sin A}$. This matches the Law of Sines correctly.
- Option B: $\frac{\sin B}{b} = \frac{\sin C}{c}$. This matches the reciprocal form of the Law of Sines correctly.
- Option C: $\frac{a}{\sin A} = \frac{b}{\sin B}$. This matches the Law of Sines correctly.
- Option D: $\frac{\sin A}{c} = \frac{\sin C}{a}$. In this equation, $\sin A$ is paired with side $c$, and $\sin C$ is paired with side $a$. Since $a$ is opposite $A$ and $c$ is opposite $C$, this pairing is incorrect.