Find the value of `(tan 495^(@))/(cot 855^(@))`

Answer

To solve the problem of finding the value of \(\frac{\tan 495^\circ}{\cot 855^\circ}\), we can follow these steps:

### Step 1: Simplify the angles
First, we need to simplify the angles \(495^\circ\) and \(855^\circ\) by reducing them within the range of \(0^\circ\) to \(360^\circ\).

- For \(495^\circ\):
\[ 495^\circ - 360^\circ = 135^\circ \]

- For \(855^\circ\):
\[ 855^\circ - 720^\circ = 135^\circ \]

Thus, we can rewrite the expression as:
\[ \frac{\tan 495^\circ}{\cot 855^\circ} = \frac{\tan 135^\circ}{\cot 135^\circ} \]

### Step 2: Evaluate \(\tan 135^\circ\) and \(\cot 135^\circ\)
Next, we evaluate \(\tan 135^\circ\) and \(\cot 135^\circ\).

- \(\tan 135^\circ\):
\[ \tan 135^\circ = -1 \quad (\text{since } 135^\circ \text{ is in the second quadrant}) \]

- \(\cot 135^\circ\):
\[ \cot 135^\circ = \frac{1}{\tan 135^\circ} = \frac{1}{-1} = -1 \]

### Step 3: Substitute the values back into the expression
Now we can substitute these values back into our expression:
\[ \frac{\tan 135^\circ}{\cot 135^\circ} = \frac{-1}{-1} = 1 \]

### Final Answer
Thus, the value of \(\frac{\tan 495^\circ}{\cot 855^\circ}\) is:
\[ \boxed{1} \]

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