Question

已知sinβ= (＜β＜π),sin(α+β)=cosα,则tan(α+β)等于(    )

A.-2                 B.2                 C.1               D.

Answer 1

解析:sin(α+β)=cosα=cos［(α+β)-β］,

即sin(α+β)=cos(α+β)cosβ+sin(α+β)sinβ,

又sinβ=,cosβ=-,

∴有sin(α+β)=-cos(α+β).

∴tan(α+β)=-2.

答案:A