已知α,β为锐角,cosα=4/5,tan(α-β=-1/3),求cosβ
人气:169 ℃ 时间:2020-06-26 11:18:02
解答
α为锐角
sin²α+cos²α=1
所以sinα=3/5
tanα=sinα/cosα=3/4
tan(α-β)=(tanα-tanβ)/(1+tanαtanβ)=-1/3
所以tanβ=13/9
sinβ/cosβ=tanβ=13/9
sinβ=13/9*cosβ
代入sin²β+cos²β=1
又β是锐角,cosβ>0
所以cosβ=9√10/50
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