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
B
nπ,nZ
C
2nππ2,nZ
D
2nπ or 2nπ+π2

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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