Find the value of `(tan25^(@))/(cot65^(@))`.

Answer

To find the value of \(\frac{\tan 25^\circ}{\cot 65^\circ}\), we can follow these steps:

### Step 1: Rewrite \(\cot 65^\circ\)
We know that \(\cot \theta = \frac{1}{\tan \theta}\). Therefore, we can rewrite \(\cot 65^\circ\) as:
\[ \cot 65^\circ = \frac{1}{\tan 65^\circ} \]

### Step 2: Substitute \(\cot 65^\circ\) into the expression
Now, substituting \(\cot 65^\circ\) into the original expression gives us:
\[ \frac{\tan 25^\circ}{\cot 65^\circ} = \tan 25^\circ \cdot \tan 65^\circ \]

### Step 3: Use the complementary angle identity
We know that:
\[ \tan(90^\circ - \theta) = \cot \theta \]
Thus, \(\tan 65^\circ\) can be expressed as:
\[ \tan 65^\circ = \tan(90^\circ - 25^\circ) = \cot 25^\circ \]

### Step 4: Substitute \(\tan 65^\circ\) back into the expression
Now we can substitute \(\tan 65^\circ\) into our expression:
\[ \tan 25^\circ \cdot \tan 65^\circ = \tan 25^\circ \cdot \cot 25^\circ \]

### Step 5: Simplify the expression
Since \(\tan \theta \cdot \cot \theta = 1\), we have:
\[ \tan 25^\circ \cdot \cot 25^\circ = 1 \]

### Final Answer
Thus, the value of \(\frac{\tan 25^\circ}{\cot 65^\circ}\) is:
\[ \boxed{1} \]