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Let's break down how to express \(\csc(x)\) and \(\cot(x)\) in terms of sine and cosine, as asked in the homework:

1. **Cosecant** (\(\csc(x)\)):  
   \[
   \csc(x) = \frac{1}{\sin(x)}
   \]

2. **Cotangent** (\(\cot(x)\)):  
   \[
   \cot(x) = \frac{\cos(x)}{\sin(x)}
   \]

Thus, the two terms in terms of \(\sin(x)\) and \(\cos(x)\) are:

- \(\csc(x) = \frac{1}{\sin(x)}\)
- \(\cot(x) = \frac{\cos(x)}{\sin(x)}\)

There is no further simplification possible, so the final answer would be:

- \(\csc(x) = \frac{1}{\sin(x)}\)
- \(\cot(x) = \frac{\cos(x)}{\sin(x)}\)

Do you need more details or have any questions about this?

Here are 5 related questions to expand on the topic:
1. What is the identity for \(\sec(x)\) in terms of sine and cosine?
2. How can you express \(\tan(x)\) using sine and cosine?
3. What is the Pythagorean identity involving \(\sin(x)\) and \(\cos(x)\)?
4. How do you differentiate \(\csc(x)\) and \(\cot(x)\)?
5. Can \(\csc(x)\) and \(\cot(x)\) be expressed using \(\tan(x)\)?

**Tip:** Always keep a list of basic trigonometric identities handy for quick reference while solving such problems.

Write the following in terms of sin(x) and cos(x), and then simplify if possible. Leave your answer in terms of sines and cosines only.

csc(x)
cot(x)

Learn how to express csc(x) and cot(x) in terms of sine and cosine with detailed explanations. This trigonometry problem covers fundamental trigonometric identities and helps you simplify the expressions. Suitable for high school students in Grades 10-12.

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