Question

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

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

• A. $2n\pi \pm \frac{\pi }{2},n\in Z$
• B. $n\pi ,n\in Z$
• C. $2n\pi -\frac{\pi }{2},n\in Z$
• D. $2n\pi or2n\pi +\frac{\pi }{2}$

Answer 1

Answer: (D)

$2n\pi or2n\pi +\frac{\pi }{2}$

clearly
$\left[f\right(\frac{\pi }{10}\left)\right]=1$
so given equation becomes
$\sin x+\cos x=1$
so $x=2n\pi$ or $2n\pi +\frac{\pi }{2}$