8. $$ \cos heta \cdot \csc heta= $$ a $$ \cot heta $$ b $$ \sin heta $$ c $$ an heta $$ d $$ \sec heta $$

Question

8. $$ \cos 	heta \cdot \csc 	heta= $$ a $$ \cot 	heta $$ b $$ \sin 	heta $$ c $$ 	an 	heta $$ d $$ \sec 	heta $$

UpStudy AI · Accepted Answer

To simplify the expression $$ \cos \theta \cdot \csc \theta $$, we can use the definitions of the trigonometric functions involved.

1. **Recall the definitions:**
   - $$ \csc \theta = \frac{1}{\sin \theta} $$

2. **Substitute the definition into the expression:**
   $$
   \cos \theta \cdot \csc \theta = \cos \theta \cdot \frac{1}{\sin \theta}
   $$

3. **Simplify the expression:**
   $$
   \cos \theta \cdot \csc \theta = \frac{\cos \theta}{\sin \theta}
   $$

4. **Recognize the result:**
   The expression $$ \frac{\cos \theta}{\sin \theta} $$ is the definition of $$ \cot \theta $$.

Thus, we have:
$$
\cos \theta \cdot \csc \theta = \cot \theta
$$

Therefore, the answer is:
**a) $$ \cot \theta $$**.
$$ \cos \theta \cdot \csc \theta = \cot \theta $$, so the answer is a) $$ \cot \theta $$.

8. \( \cos \theta \cdot \csc \theta= \) a \( \cot \theta \) b \( \sin \theta \) c \( \tan \theta \) d \( \sec \theta \)