已知cosα=4⼀5,α∈(3π⼀2,2π),tanβ=3⼀4,β∈(0,π),求cos(α-β)的值

2025-01-02 17:18:29
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回答1:

cosα=4/5,α∈(3π/2,2π),
=>sinα=-√[1-cos²α]=-√[1-(4/5)^2]=-3/5
tanβ=3/4,β∈(0,π) => β∈(0,π/2)
=> sinβ=3/5,cosβ=4/5
cos(α-β)=cosαcosβ+sinαsinβ
=(4/5)*(4/5)+(-3/5)*(3/5)
=7/25