若tan(A+B)=2tanA.求证3sinB=sin(2A+B),

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若tan(A+B)=2tanA.求证3sinB=sin(2A+B),
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若tan(A+B)=2tanA.求证3sinB=sin(2A+B),
若tan(A+B)=2tanA.求证3sinB=sin(2A+B),

若tan(A+B)=2tanA.求证3sinB=sin(2A+B),
sin(A+B)cosA=2sinAcos(A+B)=sinAcos(A+B)+sinAcos(A+B)
sin(A+B)cosA-cos(A+B)sinA=sinAcos(A+B)
sin(A+B-A)=sinAcos(A+B)
sinB=sinAcos(A+B)
sin(2A+B)=sin(A+A+B)
=sinAcos(A+B)+cosAsin(A+B)
=cosAcos(A+B)(tanA+tan(A+B))
=3cosAcos(A+B)tanA
=3sinAcos(A+B)
=3sinB