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.

Learn how to simplify the trigonometric expression 1/sin(theta) - 1/cos(theta) by finding a common denominator. This step-by-step solution covers key concepts in trigonometry, including reciprocal identities and fraction simplification. Suitable for students in Grades 10-12.

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