Question

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

Answer 1

f(x) = cos [π²]x + cos [−π²] x

\[\text{ Thus } , f(\pi) = \cos\left[ \pi^2 \right] \pi + \cos \left[ - \pi^2 \right] \pi\]
\[ \Rightarrow f(\pi) = cos \left[ 9 . 8 \right]\pi + cos\left[ - 9 . 8 \right]\pi\]
\[ \Rightarrow f(\pi) = cos  10\pi + cos 9\pi\]
\[ \Rightarrow f(\pi) = 1 + ( - 1) = 0\]