Q. 4

# If f(x) = cos2[π2]x + cos [-π2] x, where [x] denotes the greatest integer less than or equal to x, then write the value of f(π).

π2 ≈ 9.8596

So, we have [π2 ]=9 and [-π2 ]=-10

f(x)=cos 18x+ cos (-10)x

=cos 18x + cos 10x

=2 cos 14x cos4x

f(π)=2 cos 14π cos

=2×1×1

Therefore, f(π)= 2

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