Teaching NVS PGT 2024 Test Series Mathematics Relations and Functions

If f(x) = cos(loge x), then \(f(x) f(y)-\frac{1}{2}\left\{f\left(\frac{x}{y}\right)+f(x y)\right\}\) is equal to 

1
0
2
\(\frac{1}{2} f(x) f(y)\)
3
f(x + y)
4
none of these
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