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Let p(k)=(1+cos((pi)/(4k)))(1+cos((2k-1)...

Let `p(k)=(1+cos((pi)/(4k)))(1+cos((2k-1)pi)/(4k))`
`(1+cos""((2k+1)pi)/(4k))(1+cos""((4k-1)pi)/(4k))`, then

A

`P(3)=1/16`

B

`P(4)=(2-sqrt(2))/(16)`

C

`P(5)=(3-sqrt(5))/(32)`

D

`P(6)=(2-sqrt(3))/(16)`

Text Solution

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Let P(k)=(1+cos(pi/(4k))) (1+cos(((2k-1)pi)/(4k))) (1+cos(((2k+1)pi)/(4k)))(1+cos(((4k-1)pi)/(4k)))dot Then Prove that (a) P(3)=1/(16) (b) P(4)=(2-sqrt(2))/(16) (c) P(5)=(3-sqrt(5))/(32) (d) P(6)(2-sqrt(3))/(16)

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