trigonometry(5)
2011-05-30 1:27 am
Let A+B=π/4a) Express tanB in terms of tanA (I done)b) Prove that (1+tanA)(1+tanB)=2 (I done)c) Hence, prove that tan(π/8)=[(√2)/2]-1淨係做C題
回答 (1)
2011-05-30 1:38 am
✔ 最佳答案
(a) tanB= tan(π/4 - A)= (1 - tanA)/(1 + tanA)
(b) (1 + tanB) = 2/(1 + tanA)
(1 + tanA)(1 + tanB) = 2
(c) Sub. A = B = π/8
(1 + π/8)(1 + π/8) = 2
π/8 = (√2 - 1)
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