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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)))dot` Then (a)`P(3)=1/(16)` (b) `P(4)=(2-sqrt(2))/(16)` `P(5)=(3-sqrt(5))/(32)` (d) `P(6)(2-sqrt(3))/(16)`

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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 (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)

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)

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)

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(3))/(16)P(5)=(3-sqrt(5))/(32)( d) P(6)(2-sqrt(3))/(16)

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)

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)

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

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

Let F(x)=(1+sin((pi)/(2k))(1+sin(k-1)(pi)/(2k))(1+sin(2k+1)(pi)/(2k))(1+sin(3k-1)(pi)/(2k)) The value of F(1)+F(2)+F(3) is equal to