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$(1 + \cos (π / 8)) (1 + \cos (3 π / 8)) (1 + \cos (5 π / 8))$ $(1 + \cos (7 π / 8)) =$

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1/2

cos⁡(π/8)

1/8

(1+2)/22

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detailed solution

Correct option is C

We can write (1+cos⁡(π/8))(1+cos⁡(3π/8))(1−cos⁡(3π/8))(1−cos⁡(π/8))=1−cos2⁡(π/8)1−cos2⁡(3π/8)=sin2⁡π/8sin2⁡3π/8=sin2⁡π/8cos2⁡π/8=(1/4)sin2⁡π/4=1/8

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(1+cos⁡(π/8))(1+cos⁡(3π/8))(1+cos⁡(5π/8))(1+cos⁡(7π/8))=

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$(1 + \cos (π / 8)) (1 + \cos (3 π / 8)) (1 + \cos (5 π / 8))$ $(1 + \cos (7 π / 8)) =$