The expression you've provided is:

$1 + \frac{\cos x}{\sin x}$

We can simplify this expression by combining the terms under a common denominator. First, we rewrite $1$ as $\frac{\sin x}{\sin x}$, so we get:

$1 + \frac{\cos x}{\sin x} = \frac{\sin x}{\sin x} + \frac{\cos x}{\sin x}$

Now, we can combine these fractions:

$\frac{\sin x + \cos x}{\sin x}$

So, the simplified form of your expression is:

$\frac{\sin x + \cos x}{\sin x}$

Let me know if you'd like any further details or clarification!

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Tip: Remember that combining trigonometric terms often requires a common denominator, just like with regular algebraic fractions!