Find the value of `(sin 15^@)/(cos 15^@) xxtan 75^@`.

Answer

To find the value of \(\frac{\sin 15^\circ}{\cos 15^\circ} \times \tan 75^\circ\), we can follow these steps:

### Step 1: Rewrite the expression
We know that \(\frac{\sin \theta}{\cos \theta} = \tan \theta\). Therefore, we can rewrite the expression as:
\[ \tan 15^\circ \times \tan 75^\circ \]

### Step 2: Use the tangent addition formula
The tangent addition formula states that:
\[ \tan(a + b) = \frac{\tan a + \tan b}{1 - \tan a \tan b} \]
Here, we can let \(a = 15^\circ\) and \(b = 75^\circ\). Thus, we have:
\[ \tan(15^\circ + 75^\circ) = \tan 90^\circ \]
Since \(\tan 90^\circ\) is undefined, we can set up the equation:
\[ \tan 90^\circ = \frac{\tan 15^\circ + \tan 75^\circ}{1 - \tan 15^\circ \tan 75^\circ} \]

### Step 3: Analyze the equation
For \(\tan 90^\circ\) to be undefined, the denominator must be zero:
\[ 1 - \tan 15^\circ \tan 75^\circ = 0 \]
This implies:
\[ \tan 15^\circ \tan 75^\circ = 1 \]

### Step 4: Substitute back into the original expression
Now we can substitute back into our expression:
\[ \tan 15^\circ \times \tan 75^\circ = 1 \]

### Conclusion
Thus, the value of \(\frac{\sin 15^\circ}{\cos 15^\circ} \times \tan 75^\circ\) is:
\[ \boxed{1} \]