What if cos it had no number what could be the denominator

The reason is that the limit of $\cos\left(x + \frac{h}{2}\right)$ as $h \to 0$ can be found by direct substitution because the cosine function is continuous.

$$\lim_{h \to 0} \cos\left(x + \frac{h}{2}\right) = \cos\left(x + \frac{0}{2}\right) = \cos(x)$$

There is no indeterminate form (like $\frac{0}{0}$) for this part of the expression. It simply evaluates to $\cos x$.

In contrast, the term $\frac{\sin\left(\frac{h}{2}\right)}{h}$ (before rearrangement) would result in $\frac{0}{0}$ if we tried direct substitution. This is an indeterminate form, which means we need to manipulate the expression further using known limit properties, such as $\lim_{\theta \to 0} \frac{\sin\theta}{\theta} = 1$. This manipulation required creating the specific denominator $\frac{h}{2}$ for the $\sin\left(\frac{h}{2}\right)$ term.

So, the $\cos$ term doesn't need a special denominator because its limit can be found directly.