The value of `cos45^(@)-sin45^(@)` will be :

Options

A. `-1`
B. 0
C. 1
D. 2

Answer

To solve the question, we need to find the value of \( \cos 45^\circ - \sin 45^\circ \).

### Step 1: Find the value of \( \cos 45^\circ \)
We know from trigonometric ratios that:
\[ \cos 45^\circ = \frac{1}{\sqrt{2}} \]

### Step 2: Find the value of \( \sin 45^\circ \)
Similarly, we also know that:
\[ \sin 45^\circ = \frac{1}{\sqrt{2}} \]

### Step 3: Substitute the values into the expression
Now, we substitute the values of \( \cos 45^\circ \) and \( \sin 45^\circ \) into the expression:
\[ \cos 45^\circ - \sin 45^\circ = \frac{1}{\sqrt{2}} - \frac{1}{\sqrt{2}} \]

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

### Conclusion
Thus, the value of \( \cos 45^\circ - \sin 45^\circ \) is:
\[ \boxed{0} \]