已知:α,β均为锐角,且cosα=5\4,cos(α+β)=-65\16,求cosβ的值
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![已知:α,β均为锐角,且cosα=5\4,cos(α+β)=-65\16,求cosβ的值](/uploads/image/z/14950560-48-0.jpg?t=%E5%B7%B2%E7%9F%A5%3A%CE%B1%2C%CE%B2%E5%9D%87%E4%B8%BA%E9%94%90%E8%A7%92%2C%E4%B8%94cos%CE%B1%3D5%5C4%2Ccos%28%CE%B1%2B%CE%B2%29%3D-65%5C16%2C%E6%B1%82cos%CE%B2%E7%9A%84%E5%80%BC)
已知:α,β均为锐角,且cosα=5\4,cos(α+β)=-65\16,求cosβ的值
已知:α,β均为锐角,且cosα=5\4,cos(α+β)=-65\16,求cosβ的值
已知:α,β均为锐角,且cosα=5\4,cos(α+β)=-65\16,求cosβ的值
cos(A-B)=cosAcosB+sinAsinB
所以:
cosβ
=cos(α+β-β)
cos(α+β)cosβ+sin(α+β)sinβ
=(-16/65)*(4/5)+(63/65)*(3/5)
=5/13