Value of `(1-tan^(2)45^(@))/(1+ tan^(2)45^(@))` is

Options

A. `tan90^(@)`
B. 1
C. `sin 45^(@)`
D. 0

Answer

To find the value of \(\frac{1 - \tan^2 45^\circ}{1 + \tan^2 45^\circ}\), we will follow these steps:

### Step 1: Calculate \(\tan 45^\circ\)
We know that:
\[ \tan 45^\circ = 1 \]

### Step 2: Substitute \(\tan 45^\circ\) into the expression
Now, we can substitute \(\tan 45^\circ\) into the expression:
\[ \tan^2 45^\circ = 1^2 = 1 \]

### Step 3: Substitute \(\tan^2 45^\circ\) into the original expression
Now we substitute \(1\) into the expression:
\[ \frac{1 - \tan^2 45^\circ}{1 + \tan^2 45^\circ} = \frac{1 - 1}{1 + 1} \]

### Step 4: Simplify the expression
Now, simplify the expression:
\[ \frac{1 - 1}{1 + 1} = \frac{0}{2} = 0 \]

### Final Answer
Thus, the value of \(\frac{1 - \tan^2 45^\circ}{1 + \tan^2 45^\circ}\) is:
\[ \boxed{0} \]