`tan46^(@)-cot44^(@)=?`

Options

A. 0
B. 1
C. `tan46^(@)`
D. `cot44^(@)`

Answer

To solve the problem \( \tan 46^\circ - \cot 44^\circ \), we can use the relationship between tangent and cotangent.

### Step-by-Step Solution:

1. **Understand the relationship between cotangent and tangent:**
We know that:
\[ \cot \theta = \frac{1}{\tan \theta} \]
Therefore, we can rewrite \( \cot 44^\circ \) as:
\[ \cot 44^\circ = \frac{1}{\tan 44^\circ} \]

2. **Use the complementary angle identity:**
We also know that:
\[ \tan(90^\circ - \theta) = \cot \theta \]
Thus, we can express \( \cot 44^\circ \) as:
\[ \cot 44^\circ = \tan(90^\circ - 44^\circ) = \tan 46^\circ \]

3. **Substitute into the original expression:**
Now we can substitute \( \cot 44^\circ \) in our original equation:
\[ \tan 46^\circ - \cot 44^\circ = \tan 46^\circ - \tan 46^\circ \]

4. **Simplify the expression:**
This simplifies to:
\[ \tan 46^\circ - \tan 46^\circ = 0 \]

5. **Final answer:**
Therefore, the value of \( \tan 46^\circ - \cot 44^\circ \) is:
\[ 0 \]