If `f(x)=(2^x+2^(-x))/2` , then `f(x+y)f(x-y)` is equals to (a) `1/2{f(2x)+f(2y)}` (b) `1/2{f(2x)-f(2y)}` (c) `1/4{f(2x)+f(2y)}` `1/4{f(2x)-f(2y)}`

Explanation

To solve the problem, we need to find the value of \( f(x+y)f(x-y) \) where \( f(x) = \frac{2^x + 2^{-x}}{2} \).

### Step 1: Calculate \( f(x+y) \)
Using the definition of \( f(x) \):
\[ f(x+y) = \frac{2^{x+y} + 2^{-(x+y)}}{2} \]

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