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

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Correct option is C

We have −2≤sinπ2n+cosπ2n≤2⇒−2≤n2≤2⇒−22≤n≤22⇒0≤n≤8⇒n=6 only satisfies given equation

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Let n be a positive integer such that sinπ2n+cosπ2n=n2 then n =

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Ready to Test Your Skills?

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