已知α ∈(π/2,π), sin α =3 / 5 ,则tan (α+π/4)等于

发布网友 发布时间：2024-10-24 00:10

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热心网友 时间：7小时前

已知α ∈(π/2，π)， sin α =3 / 5
则cosα =√(1-sin²α )=-4/5
所以tanα=sinα/cosα=(3/5)/(-4/5)=-3/4
故tan(α+π/4)=[tanα+tan(π/4)]/[1-tanα*tam(π/4)]
=(-3/4+1)/(1+3/4)=1/7
tan(2α+π/4)=[tan(α+π/4)+tanα]/[1-tan(α+π/4)tanα]
=(1/7-3/4)/[1-(1/7)*(-3/4)]
=(4-21)/(28+3)
=-17/31

热心网友 时间：7小时前

sin α =3 / 5
因为α ∈(π/2，π)， 所以cos α=-4/5
=> tanα = -3/4
tan2α
= 2tanα/[1-(tanα)^2]
= (-3/2)/ (7/16)
= -24/7

tan (2α+π/4)
= (tan2α+1)/(1-tan2α)
= (-17/7) / (31/7)
= -17/31

热心网友 时间：7小时前

sin α =3 / 5
=> tanα = -3/4
tan2α
= 2tanα/(1-(tanα)^2)
= (-3/2)/ (7/16)
= -24/7

tan (2α+π/4)
= (tan2α+tanπ/4)/( 1- tan2αtanπ/4)
= (tan2α+1)/(1-tan2α)
= (-17/7) / (31/7)
= -17/31