`2 cos x cos y` is equal to:

Options

A. `cos(x+y)+cos(x-y)`
B. `cos(x+y)-cos(x-y)`
C. `"sin"(x+y)-"sin"(x-y)`
D. None of these

Answer

To solve the equation \( 2 \cos x \cos y \), we can use the trigonometric identity for the product of cosines. Here’s the step-by-step solution:

### Step 1: Recall the Trigonometric Identity
We start with the identity for the product of cosines:
\[ \cos A \cos B = \frac{1}{2} (\cos(A + B) + \cos(A - B)) \]
In our case, let \( A = x \) and \( B = y \). Therefore, we can rewrite \( 2 \cos x \cos y \) as follows:
\[ 2 \cos x \cos y = 2 \cdot \frac{1}{2} (\cos(x + y) + \cos(x - y)) \]

### Step 2: Simplify the Expression
Now, simplifying the expression:
\[ 2 \cos x \cos y = \cos(x + y) + \cos(x - y) \]

### Conclusion
Thus, we find that:
\[ 2 \cos x \cos y = \cos(x + y) + \cos(x - y) \]

### Final Answer
The expression \( 2 \cos x \cos y \) is equal to \( \cos(x + y) + \cos(x - y) \), which corresponds to option 1.

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