https://file.aiquickdraw.com/mathbot/file/17261128856933i6smcmb.jpg

The question asks for an equivalent expression for \(\frac{\cot(\theta)}{\cos(\theta)}\).

We can break this down by using trigonometric identities:

- \(\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}\).

Thus:

\[
\frac{\cot(\theta)}{\cos(\theta)} = \frac{\frac{\cos(\theta)}{\sin(\theta)}}{\cos(\theta)} = \frac{\cos(\theta)}{\sin(\theta)} \times \frac{1}{\cos(\theta)} = \frac{1}{\sin(\theta)}
\]

Now, \(\frac{1}{\sin(\theta)}\) is the definition of \(\csc(\theta)\).

Therefore, the correct answer is \(\csc(\theta)\), which matches the option you've selected.

Would you like more details on this?

---

Here are 5 related questions to expand your knowledge:

1. What is the identity for \(\cot(\theta)\) in terms of sine and cosine?
2. How does the Pythagorean identity relate \(\sin(\theta)\) and \(\cos(\theta)\)?
3. What is the reciprocal identity for \(\sec(\theta)\)?
4. How can you express \(\tan(\theta)\) in terms of \(\sin(\theta)\) and \(\cos(\theta)\)?
5. What is the difference between \(\csc(\theta)\) and \(\sec(\theta)\)?

**Tip:** Always keep the basic trigonometric identities in mind, as they simplify many expressions quickly.

Which of the following is equivalent to cot(θ)/cos(θ)?

Understand how to solve the trigonometric identity problem by simplifying cot(θ)/cos(θ). This problem uses key concepts like cotangent and cosecant identities. Suitable for high school students learning trigonometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation