风过无痕雨无声
幼苗
共回答了13个问题采纳率:92.3% 举报
(1)
sin3α/sinα=13/5
sin3α/sinα = sin(α+2α)/sinα
=(sinαcos2α+sin2αcosα)/sinα
= [sinα(2cos^2α-1)+2sinαcosαcosα]/sinα
= 2cos^2α-1+2cos^2α
= 4cos^2α-1 = 13/5
cos^2α=9/10
tan^2α=sin^2α/cos^2α = (1-cos^2α)/cos^2α = (1-9/10)/(9/10) = 1/9
α为第四象限
tanα = -1/3
(2)
α为锐角,则tanα=1/3
又:tanβ=2+√5
tan2β=2tanβ/(1-tan^2β) = 2(2+√5)/[-4(2+√5)] = -1/2
tan(α+2β) = (tanα+tan2β)/(1-tanαtan2β) = (1/3-1/2)/(1/3+1/3*1/2) = -1/3
α、β为锐角,α+2β为一、二或三象限角,tan(α+2β) <0,∴α+2β为第二象限角
∴α+2β = π-arctan(1/3)
1年前
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