First slide

Trigonometric equations

Question

Let n be a positive integer such that $\sin (\frac{π}{2 n}) + \cos (\frac{π}{2 n}) = \frac{\sqrt{n}}{2}$ then n =

Easy

A

2
B

3
C

6
D

8

Solution

$W e h a v e - \sqrt{2} \leq \sin (\frac{π}{2 n}) + \cos (\frac{π}{2 n}) \leq \sqrt{2}$
$\Rightarrow - \sqrt{2} \leq \frac{\sqrt{n}}{2} \leq \sqrt{2}$
$\Rightarrow - 2 \sqrt{2} \leq \sqrt{n} \leq 2 \sqrt{2}$
$\Rightarrow 0 \leq n \leq 8$
$\Rightarrow n = 6$ only satisfies given equation

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