(a) By using the formula sinAcosA = 1/2 sin2A, prove that cosθcos2θcos4θ = 1/8 sin8θcscθ where sinθ≠0.
(b) Hence, find the value of cos20cos40cos80 without using a calculator.
F.4 trigonometry===
2010-03-08 12:05 am
回答 (1)
2010-03-08 12:53 am
✔ 最佳答案
a)sinAcosA = 1/2 sin2AcosA = (1/2)sin2A / sinA ; so
cosθcos2θcos4θ
= [ (1/2)sin2θ / sinθ ] * [(1/2)sin4θ / sin2θ] * [(1/2)sin8θ / sin4θ]
= (1/8)sin8θ / sinθ
= (1/8) sin80 cscθ
b)cos20cos40cos80
= (1/8)sin(8*20) csc20
= (1/8) sin160 / sin20
= (1/8) sin (180 - 160) / sin20
= 1/8
收錄日期: 2021-04-13 17:08:29
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