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 4π
=2×1×1
Therefore, f(π)= 2