Show this is an identity.
sin (A+B)/sin(A-B)=cot A + cot B/cot A - cot B.

Question

anonymous · Answer

you may want write cot as cos/sin
RHS = cot A + cot B/cot A - cot B.
numerator is  cosA      cosB
                     ---   + -------
                     sinA       sinB
cosA  sinB + sinAcosB

--------------------
       sin A  sin B
denominator is  cosA      cosB
                     ---   -  -------
                     sinA       sinB
cosA  sinB - sinAcosB
--------------------
       sin A  sin B
now the rhs is ... cosA  sinB + sinAcosB
                         ------------------
                          cosA  sinB - sinAcosB

    sin (A+B)
=  ---------   = LHS
    sin(A-B)