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
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![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](/uploads/image/z/11695851-27-1.jpg?t=%E5%B7%B2%E7%9F%A5%CE%B1%2C%CE%B2%E5%B1%9E%E4%BA%8E%280%2C%CF%80%2F2%29%2C%E4%B8%94sin%28%CF%80%2B%CE%B1%29%3D-4%2F5%2Ccos%28%CE%B1%2B%CE%B2%29%3D%3D5%2F13.%E6%B1%82%3A%281%29cos2%CE%B1%E7%9A%84%E5%80%BC%282%29cos%CE%B2%E7%9A%84%E5%80%BC)
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