The value of `(1-tan^(2)15^(@))/(1+tan^(2)15^(@))` is

Options

A. 1
B. `sqrt(3)`
C. `sqrt(3)/2`
D. 2

Answer

To solve the expression \((1 - \tan^2 15^\circ) / (1 + \tan^2 15^\circ)\), we can use the trigonometric identity related to cosine.

### Step-by-Step Solution:

1. **Identify the Formula**:
We will use the identity:
\[ \frac{1 - \tan^2 \theta}{1 + \tan^2 \theta} = \cos 2\theta \]
Here, \(\theta = 15^\circ\).

2. **Substitute the Value of \(\theta\)**:
Substitute \(15^\circ\) into the formula:
\[ \frac{1 - \tan^2 15^\circ}{1 + \tan^2 15^\circ} = \cos(2 \times 15^\circ) = \cos 30^\circ \]

3. **Calculate \(\cos 30^\circ\)**:
We know that:
\[ \cos 30^\circ = \frac{\sqrt{3}}{2} \]

4. **Final Result**:
Therefore, the value of \(\frac{1 - \tan^2 15^\circ}{1 + \tan^2 15^\circ}\) is:
\[ \frac{\sqrt{3}}{2} \]

### Conclusion:
The final answer is:
\[ \frac{1 - \tan^2 15^\circ}{1 + \tan^2 15^\circ} = \frac{\sqrt{3}}{2} \]