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If f(x) = cos ([pi]x) +cos [pi x], where...

If f(x) `= cos ([pi]x) +cos [pi x]`, where [] is the greatest integer function, then `f((pi)/(2))` is equal to

A

`cos3`

B

0

C

`cos 4`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`f (x) = cos [pi] x + cos[pix]`
`f((pi)/(2)) = cos([pi].(pi)/(2)] + cos[(pi^(2))/(2)]= cos.(3pi)/(2)+ cos 4 = cos4`
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