trigonometry

👨🏻‍🏫 學術台數學

Larry

2011-05-24 2:42 am

It is given that (sinB/sinA)=cos(A+B).Prove that tan(A+B)=2tanA

回答 (1)

用戶2053

2011-05-24 3:45 am

✔ 最佳答案

sinB / sinA = cos(A+B)sinB / sinA = cosAcosB - sinAsinB1 = sinAcosA cosB/sinB - sin²A1 / cos²A = sinA/cosA cosB/sinB - sin²A /cos²Atan²A + 1 = tanA / tanB - tan²A2tan²AtanB + tanB = tanA2tan²AtanB + tanA + tanB = 2tanAtanA + tanB = 2tanA (1 - tanA tanB)(tanA + tanB) / (1 - tanA tanB) = 2tanAtan(A+B) = 2tanA

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