NTA Abhyas JEE Main2020MathematicsFunctionsPractice

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

Options

A− 1
B1 2
C− 2
D0

Correct answer

D. 0

Step-by-step solution

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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