Answer
$C$ is not valid.
Work Step by Step
This exercise tests your understanding of the law of sines, which states in any triangle $ABC$, with sides $a$, $b$ and $c$
$$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$$
From the law of sines, we can deduce $$\frac{a}{\sin A}=\frac{b}{\sin B}$$
$B$ is valid.
With transformation, we also have
$$\frac{a}{b}=\frac{\sin A}{\sin B}$$
$A$ is valid.
Also, we can rewrite as follows
$$\frac{\sin A}{a}=\frac{\sin B}{b}$$
$D$ is valid.
However, there is no way to change the equation into the one that is shown in $C$. In fact, from the law of sines:
$$a\sin B=b\sin A$$
Yet, from $C$:
$$ab=\sin A\sin B$$
That means they are totally different from each other. $C$ is not valid.
