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To prove : cos(π/5) cos(2π/5) cos(4π/5) cos(8π/5) = -1/16

To prove : cos(π/5) cos(2π/5) cos(4π/5) cos(8π/5) = -1/16

Grade:11

1 Answers

Aditya Gupta
2081 Points
4 years ago
Given cos(π/5) cos(2π/5) cos(4π/5) cos(8π/5) [ multiply and divide by 2sin(π/5) ] ⇒ 2sin(π/5)cos(π/5) cos(2π/5) cos(4π/5) cos(8π/5) / 2sin(π/5) [ ∴2sin A cos A = sin 2A ] ⇒ 2sin (2π/5)cos(2π/5) cos(4π/5) cos(8π/5) / 22sin(π/5) [ multiply and divide by 2] ⇒ 2sin (4π/5)cos(4π/5) cos(8π/5) / 4x 2sin(π/5) [ multiply and divide by 2] ⇒ 2sin (8π/5) cos(8π/5) / 8x 2sin(π/5) [ multiply and divide by 2] ⇒ sin (16π/5) / 16sin(π/5) ⇒ sin (3π + π/5) / 16sin(π/5) ⇒- sin (π/5) / 16sin(π/5) = - 1 / 16
kindly approve :=)

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