The expression you provided is:

$\frac{1}{\sin(\theta)} - \frac{1}{\cos(\theta)}$

We can simplify this by finding a common denominator:

1. The common denominator between $\sin(\theta)$ and $\cos(\theta)$ is $\sin(\theta)\cos(\theta)$.

2. Rewrite each term using the common denominator:

$\frac{\cos(\theta)}{\sin(\theta)\cos(\theta)} - \frac{\sin(\theta)}{\sin(\theta)\cos(\theta)}$

3. Combine the two fractions:

$\frac{\cos(\theta) - \sin(\theta)}{\sin(\theta)\cos(\theta)}$

So, the simplified form of the expression is:

$\frac{\cos(\theta) - \sin(\theta)}{\sin(\theta)\cos(\theta)}$

Would you like further details on trigonometric simplifications, or any other questions?

Related Questions:

1. What happens if $\theta = 45^\circ$ in this expression?
2. How do we simplify $\frac{1}{\sin(\theta)} + \frac{1}{\cos(\theta)}$?
3. Can we express $\sin(\theta)$ and $\cos(\theta)$ in terms of other trigonometric functions?
4. How do we handle this expression if $\theta$ is an unknown angle?
5. What real-world problems involve these trigonometric expressions?

Tip:

Always consider factoring or using identities like Pythagoras’ theorem for trigonometric simplifications.