15问答网 > 已知α,β均为锐角,且sinα=4⼀5,tanβ=1⼀7,求α-β的值、、求过程、、、

已知α,β均为锐角,且sinα=4⼀5,tanβ=1⼀7,求α-β的值、、求过程、、、

2025-03-25 19:16:51
推荐回答（1个）
回答1：

sinα=4/5, => cosα=3/5
tanβ=1/7, => sinβ= 1/√8 , cosβ= 7/√8

sin(α-β) = sinαcosβ-cosαsinβ
=(4/5)(7/√8)-(3/5)(1/√8)
= 5/√8
= 5√2/8
α-β = arcsin(5√2/8)

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