IF `X=tan 40^@` then the value of `2 tan 50^@` will be

Options

A. `2/X`
B. `2X`
C. `1/X`
D. `1/(2X)`

Answer

To solve the problem, we need to find the value of \( 2 \tan 50^\circ \) given that \( X = \tan 40^\circ \).

### Step-by-Step Solution:

1. **Understanding the Relationship Between Angles**:
We know that \( 40^\circ \) and \( 50^\circ \) are complementary angles because:
\[ 40^\circ + 50^\circ = 90^\circ \]
This means that:
\[ \tan 40^\circ = \cot 50^\circ \]

2. **Expressing \( \tan 50^\circ \)**:
Since \( \tan 40^\circ = \cot 50^\circ \), we can express \( \tan 50^\circ \) in terms of \( \tan 40^\circ \):
\[ \tan 50^\circ = \frac{1}{\tan 40^\circ} \]

3. **Substituting the Value of \( X \)**:
Given that \( X = \tan 40^\circ \), we can substitute this into our equation:
\[ \tan 50^\circ = \frac{1}{X} \]

4. **Finding \( 2 \tan 50^\circ \)**:
Now, we can find \( 2 \tan 50^\circ \):
\[ 2 \tan 50^\circ = 2 \cdot \frac{1}{X} = \frac{2}{X} \]

5. **Final Answer**:
Therefore, the value of \( 2 \tan 50^\circ \) is:
\[ \frac{2}{X} \]