Let `P(k)=(1+cospi/(4k))` `(1+cos((2k-1)pi)/(4k))` `(1+cos((2k+1)pi)/(4k))(1+cos((4k-1)pi)/(4k))dotT h e n` `P(3)=1/(16)` (b) `P(4)=(2-sqrt(2))/(16)` `P(5)=(3-sqrt(5))/(32)` (d) `P(6)(2-sqrt(3))/(16)`

Explanation

To solve the problem, we need to evaluate the function \( P(k) \) defined as:

\[ P(k) = \left(1 + \cos\left(\frac{\pi}{4k}\right)\right) \left(1 + \cos\left(\frac{(2k-1)\pi}{4k}\right)\right) \left(1 + \cos\left(\frac{(2k+1)\pi}{4k}\right)\right) \left(1 + \cos\left(\frac{(4k-1)\pi}{4k}\right)\right) \]

We will calculate \( P(3) \), \( P(4) \), \( P(5) \), and \( P(6) \) step by step.

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