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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).
Solution
f(x) = cos [π2]x + cos [−π2] x
\[ \Rightarrow f(\pi) = cos \left[ 9 . 8 \right]\pi + cos\left[ - 9 . 8 \right]\pi\]
\[ \Rightarrow f(\pi) = cos 10\pi + cos 9\pi\]
\[ \Rightarrow f(\pi) = 1 + ( - 1) = 0\]
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