α,β均为锐角,tanα=7,cosβ=2根号5⼀5,求α+2β?

2025-06-22 05:43:53
推荐回答(1个)
回答1:

tanα=7
cosβ=2√5/5
tanβ = √5/(2√5) =1/2
tan2β
= 2tanβ/[ 1- (tanβ)^2]
=1/( 1 - 1/4)
=4/3
tan(α+2β)
=(tanα+tan2β)/( 1- tanα.tan2β)
=( 7 + 4/3) /[ 1 - (7)(4/3) ]
=( 25/3)/( -25/3)
=-1
α+2β = 3π/4