If f ( x ) = cos ( ln x ) , then f ( x ) ⋅ f ( y ) − 1 2 [ f ( x y ) + f ( x y ) ] is equal to

Question

If f ( x ) = cos ( ln x ) , then f ( x ) ⋅ f ( y ) − 1 2 [ f ( x y ) + f ( x y ) ] is equal to, − 1, 1 2, − 2, 0

MARKS App · Accepted Answer

Given, f ( x ) = cos ( ln x ) Hence, f ( x ) ⋅ f ( y ) − 1 2 [ f ( x y ) + f ( x y ) ] = cos ( ln x ) ⋅ cos ( ln y ) − 1 2 [ cos ( ln x − ln y ) + cos ( ln x + ln y ) ] = cos ( ln x ) ⋅ cos ( ln y ) − 1 2 [ ( 2 cos ( ln x ) ⋅ cos ( ln y ) ] = cos ( ln x ) ⋅ cos ( ln y ) − cos ( ln x ) ⋅ cos ( ln y ) = 0

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