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Question

If, f(x)=cos[π2]x+cos[π2]x, where [x] stands for greatest integer function, then


A

f(π2)=1

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B

f(π)=1

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C

f(π)=0

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D

f(π4)=2

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Solution

The correct option is C

f(π)=0


f(x)=cos[π2]x+cos[π2]x
f(x) = cos 9x + cos (-10)x
f(x) = cos 9x + cos 10 x
f(π2)=01=1
f (π) = -1 + 1 = 0
f (π) = -1 + 1 = 0
f(π4)=12+0=12


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