The value of `(1+cospi/8)(1+cos(3pi)/8)(1+cos(5pi)/8)(1+cos(7pi)/8)i s` (a)1/4 (b) 3/4 (c) 1/8 (d) 3/8

Explanation

`cos(7/8pi)=cos(pi-pi/8)=-cospi/8`

`cos(5/8pi)=cos(pi-3/8pi)=-cos3/8pi`

`(1+cospi/8)(1-cospi/8)(1+cos3/8pi)(1-cos3/8pi)`

`=[1-cos^2pi/8][1-cos^2 3/8pi]`

`=sin^2pi/8*sin^2 3/8pi`

`1/4(2sin^2pi/8)(2sin^2 3/8pi)`

`1/4[(1-cospi/4)(1-cos3/4pi)]`

`1/4[(1-1/sqrt2)(1+1/sqrt2)]`

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