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Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions1 Mark
Question
If $\text{f(x)}=\cos\big[\pi^2\big]\text{x}+\cos\big[-\pi^2\big]\text{x},$ where[x] denotes the greatest integer less than or equal to x, then write the value of $\text{f}(\pi)$
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Answer

We have,
$\text{f}(\text{x})=\cos[\pi^2]\text{x}+\cos[-\pi^2]\text{x}$
$\therefore \text{f}(\pi)= \cos[\pi^2]\pi+\cos[-\pi^2]\pi$
$=0+0$ $[ \because\cos\text{n}\pi=0]$
$=0$
$\therefore\text{ f}(\pi)= 0$

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