Question

Let $n$ be a positive integer such that $\sin \left(\frac{\pi }{2^n}\right)+\cos \left(\frac{\pi }{2^n}\right)=\frac{\sqrt{n}}{2},$ then

• A. $6\le n\le 8$
• B. $4<n\le 8$
• C. $4\le n<8$
• D. $4<n<8$

Answer 1

Answer: (C)

$4\le n<8$

$\delta \frac{3}{2n}+\cos \frac{3}{2n}=\frac{\sqrt{n}}{2}$

$1+2\cos \frac{\pi }{2n}\sin \frac{3}{2n}=\frac{h}{2}$

$\sin \frac{\pi }{2^{n1}}=(\frac{n}{4}-1)$

put the value of $n$ and check only on option

$4\le n<8$