Let `n` be a positive integer such that `sinpi/(2n)+cospi/(2n)=(sqrt(n))/2dot` Then `6lt=nlt=8` (b) `4 ltnle8` c) `4lenle8` d) `4ltnlt8`

Explanation

To solve the equation \( \sin\left(\frac{\pi}{2n}\right) + \cos\left(\frac{\pi}{2n}\right) = \frac{\sqrt{n}}{2} \), we will follow these steps:

### Step 1: Square both sides
To eliminate the sine and cosine terms, we square both sides of the equation:
\[ \left(\sin\left(\frac{\pi}{2n}\right) + \cos\left(\frac{\pi}{2n}\right)\right)^2 = \left(\frac{\sqrt{n}}{2}\right)^2 \]
This gives us:
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