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Question
If f(x) = sin [π2] x + sin [−π]2 x, where [x] denotes the greatest integer less than or equal to x, then
Options
(a) f(π/2) = 1
(b) f(π) = 2
(c) f(π/4) = −1
(d) None of these
Solution
(a) f(π/2) = 1
f(x) = sin [π2] x + sin [−π2]x
\[\Rightarrow f(x) = \sin \left[ 9 . 8 \right]x + \sin \left[ - 9 . 8 \right]x\]
\[ \Rightarrow f(x) = \sin 9x - \sin 10x\]
\[f\left( \frac{\pi}{2} \right) = \sin 9 \times \frac{\pi}{2} - \sin 10 \times \frac{\pi}{2}\]
\[ \Rightarrow f\left( \frac{\pi}{2} \right) = 1 - 0 = 1\]
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