Question

If f(x) = cos(ln x), then f(x) f(y) -$\frac{1}{2}\left\lbrack f\left( \frac{x}{y} \right) + f(xy) \right\rbrack$ has the value

• A. −1
• B. ½
• C. −2
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

f(x) = cos(log x) f(x) f(y) − $\frac{1}{2}\left\lbrack f\left( \frac{x}{y} \right) + f(xy) \right\rbrack$

= cos(log x) cos (log y) $\frac{1}{2}$ [cos (log x – logy) + cos (log x + log y)]

= cos (log x) cos (log y) -$\frac{1}{2}$ [2 cos(log x) cos (log y)] = 0

∴ (4) is the correct alternative.