If `f(x) = cos(log x)` then `f(x)f(y)-1/2[f(x/y)+f(xy)]` has the value

Options

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

Explanation

To solve the problem, we need to evaluate the expression \( f(x)f(y) - \frac{1}{2}[f(x/y) + f(xy)] \) given that \( f(x) = \cos(\log x) \).

### Step-by-Step Solution:

1. **Identify the Functions**:
- We have \( f(x) = \cos(\log x) \).
- Therefore, \( f(y) = \cos(\log y) \).
- For \( f(x/y) \), we have:
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