α,β∈(0,π),tan(α/2)=1/2且sin(α+β)=5/13,求cosβ

tanα=2tan(α/2)/(1-(tan(α/2)^2))=2*1/2/(1-(1/2)^2)=4/3即 sinα/cosα=4/3α,β∈(0,π)所以sinα=4/5cosα=3/5tanα=4/3>1,所以 α>π/40α+β>π/2所以 cos(α+β)