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Question

Let f(x)=cos[π2]x+cos[π2]x,where [ .] represents greatest integer function,then f(π2)=1 and f(π)=?

A
-1
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B
1
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C
0
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D
π
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Solution

The correct option is C 0

Weknowthat,π=3.14Then,(π)(π)9somethingi.e9<π2<10Now,f(x)=cos(9x)+cos(10x),orf(x)=cos(9x)+cos(10x)[As.cos(x)=cosx]Now,f(π2)=cos(9π2)+cos(10π2)=cos(9π2)+cos(5π2)=cos(4π+π2)+cos(4π+π)=cos(π2)+cos(π)=01=1Similarly,f(π)=cos(9π)+cos(10π)=cos(9π)+cos(10π)=cos(8π+π)+cos(10π)=cos(π)+cos(0)=1+1=0


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