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Question


 Let $$[\ {x}]=$$ the greatest integer less than or equal to $$\ {x}$$ and let $$\ {f}(\ {x})=\sin \ {x}+ \cos x$$, then the most


general solutions of $$\displaystyle \ {f}(\ {x})=[\ {f}(\frac{\pi}{10})]$$ are



A
2nπ±π2,nZ
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B
nπ,nZ
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C
2nππ2,nZ
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D
2nπ or 2nπ+π2
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Solution

The correct option is B $$2\displaystyle \mathrm{n}\pi \mathrm\ {or}\ 2\mathrm{n}\pi+\frac{\pi}{2}$$
clearly 
$$[f(\dfrac{\pi}{10})] = 1 $$
so given equation becomes
$$ \sin x + \cos x = 1$$
so $$ x = 2n\pi$$ or $$2n\pi + \dfrac{\pi}{2}$$

Mathematics

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