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Maths-

General

Easy

Question

If $f space left parenthesis x right parenthesis equals cos space left parenthesis log space x right parenthesis comma text then end text f open parentheses x squared close parentheses times f open parentheses y squared close parentheses minus 1 half open square brackets f open parentheses x squared y squared close parentheses plus f open parentheses x squared over y squared close parentheses close square brackets equals$

$- 2$
$- 1$
$\frac{1}{2}$
0

hint Hint:

In the given question we have to find the value of $f open parentheses x squared close parentheses times f open parentheses y squared close parentheses minus 1 half open square brackets f open parentheses x squared y squared close parentheses plus f open parentheses x squared over y squared close parentheses close square brackets$ for this we will put the values and get the answer.

The correct answer is: 0

For, $f space left parenthesis x right parenthesis equals cos space left parenthesis log space x right parenthesis$
$f open parentheses x squared close parentheses times f open parentheses y squared close parentheses minus 1 half open square brackets f open parentheses x squared y squared close parentheses plus f open parentheses x squared over y squared close parentheses close square brackets equals$ cos (log $x squared$ ). cos (log $y squared$ ) $minus$ $1 half open square brackets cos space log space left parenthesis x squared. y squared right parenthesis plus cos space log space open parentheses x squared over y squared close parentheses close square brackets$
$equals cos space log space x squared. space cos space log space y squared minus 1 half open square brackets cos left parenthesis log space x squared plus log space y squared right parenthesis plus cos left parenthesis log space x squared minus log space y squared right parenthesis close square brackets equals cos space log space x squared. space cos space log space y squared minus space cos space log space x squared. space cos space log space y squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets cos space x. space cos space y equals 1 half open square brackets cos open parentheses x plus y close parentheses plus cos open parentheses x minus y close parentheses close square brackets close square brackets equals 0$

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