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Nadusha1986 [10]
3 years ago
7

Hello! Please help!! I really need this.​

Mathematics
2 answers:
Liono4ka [1.6K]3 years ago
7 0

Answer:

<u>Lets show that:</u>

  • cos x cos 2x cos 4x cos 8x = sin 16x / 16 sinx

<u>Use formula:</u>

  • sin 2x = 2 sin x cos x

<u>Multiply LHS by 2sinx/2sinx:</u>

  • 2sinx cos x cos 2x cos 4x cos 8x / 2 sin x =
  • sin 2x  cos 2x cos 4x cos 8x / 2 sin x =
  • 2sin 2x cos 2x cos 4x cos 8x / 4 sin x =
  • sin 4x  cos 4x cos 8x / 4 sin x =
  • 2sin 4x  cos 4x cos 8x / 8 sin x =
  • sin 8x cos 8x / 8 sin x =
  • 2 sin 8x cos 8x / 16 sin x =
  • sin 16x / 16 sin x

<u>Now, we can easily find that:</u>

  • sin (16*2π/15) = sin (2π/15)

<u>Coming back to the original equation, we get:</u>

  • cos (2π/15) cos (4π/15) cos (8π/15) cos (16π/15) = sin (16*2π/15) / 16 sin (2π/15)
  • cos (2π/15) cos (4π/15) cos (8π/15) cos (16π/15) = 1/16
IrinaVladis [17]3 years ago
4 0

its a i did this a while ago

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