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Prove that cos 20֯ cos 40֯ cos 60֯ cos 80֯ = 1/16

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Answer:

  • cos 20֯ cos 40֯ (1/2) cos 80֯
  • 1/4 (2 cos 40֯ cos 20֯) cos 80֯
  • ¼ (cos 60֯ + cos 20֯) cos 80֯ 
  • ¼ cos 60֯ cos 80 + ¼ cos 20 cos 80
  • ¼ ½ cos 80 + ¼* 1/2*(2 cos 20 cos 80)
  • 1/8 cos 80 + 1/8 (cos 100 + cos 60)
  • 1/8 cos 80 + 1/8 (cos 180 – 80) + 1/8 cos 60
  • 1/8 cos 80 – 1/8 cos 80 + 1/8*1/2
  • 1/16
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