If cos x = `1/3`. Then, what is sinx. cotx. cosec x. tan x equal to?

Options

A. `2/3`
B. `3/2`
C. 2
D. 1

Answer

To solve the problem, we need to find the value of \( \sin x \cdot \cot x \cdot \csc x \cdot \tan x \) given that \( \cos x = \frac{1}{3} \).

### Step-by-Step Solution:

1. **Identify the trigonometric identities**:
- We know that:
\[ \cot x = \frac{1}{\tan x} \]
\[ \csc x = \frac{1}{\sin x} \]
- Therefore, we can rewrite the expression \( \sin x \cdot \cot x \cdot \csc x \cdot \tan x \) using these identities.

2. **Rewrite the expression**:
- Substitute the identities into the expression:
\[ \sin x \cdot \cot x \cdot \csc x \cdot \tan x = \sin x \cdot \left(\frac{1}{\tan x}\right) \cdot \left(\frac{1}{\sin x}\right) \cdot \tan x \]

3. **Simplify the expression**:
- Notice that \( \tan x \) and \( \cot x \) will cancel out:
\[ = \sin x \cdot \frac{1}{\tan x} \cdot \frac{1}{\sin x} \cdot \tan x = 1 \]

4. **Final result**:
- The final value of \( \sin x \cdot \cot x \cdot \csc x \cdot \tan x \) is:
\[ = 1 \]

### Conclusion:
Thus, the answer is \( 1 \).