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Question

If f(x)=cos(π2]x+cos(π2]x, where [x] stands for the 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)=1
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Solution

The correct options are
A f(π2)=1
C f(π)=0
f(x)=cos(π2]x+cos(π2]xWe know, 9<π2<10 and 10<π2<9[π2]=9, [π2]=10f(x)=cos 9x +cos (10x)f(x)=cos (9x) +cos (10x)( cos(x) = cos(x))If x=π2, f(π2)=cos (9π2)+cos (5π)=1 (True)If x=π, f(π)=cos (9π)+cos (10π)=0 (False)If x=π, f(π)=cos (9π)+cos (10π)=0 (True)If x=π4, f(π4)=cos (9π4)+cos (10π4)=12 (False)

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