`cos9^@-sin9^@=`

Options

A. `(5+sqrt5)/(4)`
B. `(sqrt(5-sqrt5))/(2)`
C. `-(sqrt(5-sqrt5))/(2)`
D. none of these

Answer

To solve the expression \( \cos 9^\circ - \sin 9^\circ \), we will first calculate the values of \( \cos 9^\circ \) and \( \sin 9^\circ \) using a calculator or trigonometric tables.

### Step 1: Calculate \( \cos 9^\circ \) and \( \sin 9^\circ \)

Using a calculator:
- \( \cos 9^\circ \approx 0.9877 \)
- \( \sin 9^\circ \approx 0.1564 \)

### Step 2: Substitute the values into the expression

Now we substitute these values into the expression:

\[ \cos 9^\circ - \sin 9^\circ = 0.9877 - 0.1564 \]

### Step 3: Perform the subtraction

Now, we perform the subtraction:

\[ 0.9877 - 0.1564 = 0.8313 \]

### Step 4: Round the result

We can round this result to two decimal places:

\[ 0.8313 \approx 0.83 \]

### Conclusion

Thus, the value of \( \cos 9^\circ - \sin 9^\circ \) is approximately \( 0.83 \).