已知α,β属于(0,π/2),且sin(π+α)=-4/5,cos(α+β)==5/13.求:(1)cos2α的值(2)cosβ的值

已知α,β属于(0,π/2),且sin(π+α)=-4/5,cos(α+β)==5/13.求:(1)cos2α的值(2)cosβ的值
已知α,β属于(0,π/2),且sin(π+α)=-4/5,cos(α+β)==5/13.求:(1)cos2α的值(2)cosβ的值

已知α,β属于(0,π/2),且sin(π+α)=-4/5,cos(α+β)==5/13.求:(1)cos2α的值(2)cosβ的值
(1)sin(π+α)=-sinα=-4/5,则sinα=4/5,cos2α=1-2(sinα)^2=1-16/25=9/25.
(2)cosα=3/5
cos(α+β)=5/13>0,则0<α+β<π/2,即sin(α+β)=12/13.
cosβ=cos[(α+β)-α]=cos(α+β)cosα+sin(α+β)sinα=(5/13)*(3/5)+(12/13)*(4/5)=63/65