If \(f(x) = \cos[\pi^2]x + \cos[-\pi^2]x\), where \([.]\) stands for the greatest integer function, then \(f\left(\frac{\pi}{2}\right)\) is:
\[ f(x) = \cos\left[\pi^2\right]x + \cos\left[-\pi^2\right]x \] \[ f(x) = \cos\left[9.85\right]x + \cos\left[-9.85\right]x \] \[ f(x) = \cos9x + \cos10x \] Thus: \[ f\left(\frac{\pi}{2}\right) = 0 - 1 = -1 \]
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