若α,β均为锐角,且sinα=根号下5/5,tanβ=1/3,则α+β=?

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若α,β均为锐角,且sinα=根号下5/5,tanβ=1/3,则α+β=?

若α,β均为锐角,且sinα=根号下5/5,tanβ=1/3,则α+β=?
若α,β均为锐角,且sinα=根号下5/5,tanβ=1/3,则α+β=?

若α,β均为锐角,且sinα=根号下5/5,tanβ=1/3,则α+β=?
sinα=√5/5
cosα=2√5/5
tanβ=1/3
sinβ=√10/10
cosβ=3√10/10
sin(α+β)
=sinαcosβ+cosαsinβ
=√5/5*3√10/10+2√5/5*√10/10
=3√50/50+2√50/50
=5√50/50
=25√2/50
=√2/2
α+β=45°或135°
因为tanβ=1/3,β