Evaluate the following limit: `lim_(x->a)(cos x-cos a)/(sqrt(x)-sqrt(a))`

Explanation

To evaluate the limit \( \lim_{x \to a} \frac{\cos x - \cos a}{\sqrt{x} - \sqrt{a}} \), we can follow these steps:

### Step 1: Apply the Cosine Difference Formula
We know that the difference of cosines can be expressed using the sine function:
\[ \cos x - \cos a = -2 \sin\left(\frac{x + a}{2}\right) \sin\left(\frac{x - a}{2}\right) \]
Thus, we can rewrite the limit as:
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