Prove that sinB/sinA=sin(2A+B)/sinA-2cos(A+B)

Steps to Prove sinB/sinA=sin(2A+B)/sinA-2cos(A+B)

Take R.H.S sin(2A+B)/sinA-2cos(A+B) 

=sin(2A+B)-2cos(A+B).sinA/sinA

=sin(2A+B)-{sin(A+B+A)-sin(A+B-A)}/sinA    [2.cosC.sinD=sin(C+D)-sin(C-D)]

=sin(2A+B)-{sin(2A+B)-sinB}/sinA

=sin(2A+B)-sin(2A+B)+sinB/sinA

=sinB/sinC= L.H.S

∴ Hence we proved that sinB/sinA=sin(2A+B)/sinA-2cos(A+B)

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