The expression you provided is \( \tan(a) + \cot(a) \). To simplify this, we can express \( \cot(a) \) in terms of \( \tan(a) \).

\[
\cot(a) = \frac{1}{\tan(a)}
\]

Now, substitute this into the original expression:

\[
\tan(a) + \cot(a) = \tan(a) + \frac{1}{\tan(a)}
\]

This can be written as:

\[
\tan(a) + \frac{1}{\tan(a)} = \frac{\tan^2(a) + 1}{\tan(a)}
\]

So, the expression simplifies to:

\[
\tan(a) + \cot(a) = \frac{\tan^2(a) + 1}{\tan(a)}
\]

This is the simplified form of the expression.

Would you like more details or have any questions?

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Here are 5 related questions you might find interesting:
1. What is the value of \( \tan(a) + \cot(a) \) when \( a = 45^\circ \)?
2. How does the identity \( \tan(a) \cdot \cot(a) = 1 \) relate to this expression?
3. Can you express \( \tan(a) + \cot(a) \) using sine and cosine?
4. How would the expression change if we used \( \tan^2(a) + \cot^2(a) \) instead?
5. What is the behavior of the expression \( \tan(a) + \cot(a) \) as \( a \) approaches \( 0 \) or \( \frac{\pi}{2} \)?

**Tip:** Understanding how trigonometric identities relate to each other can greatly simplify solving complex trigonometric equations.

Learn how to simplify and calculate the expression tan(a) + cot(a) using trigonometric identities. Understand the relationship between tan(a), cot(a), and their simplified form. Suitable for high school students studying trigonometry.

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