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).

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Solution

f(x) = cos [π²]x + cos [−π²] x
$Thus, f (π) = \cos [π^{2}] π + \cos [- π^{2}] π \Rightarrow f (π) = c o s [9.8] π + c o s [- 9.8] π \Rightarrow f (π) = c o s 10 π + c o s 9 π \Rightarrow f (π) = 1 + (- 1) = 0$

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