Prove that sinA+sinB/sinA-sinB=tan(A+B)/2.cot(A+B)/2

Steps to prove sinA+sinB/sinA-sinB=tan(A+B)/2.cot(A+B)/2

Take L.H.S sinA+sinB/sinA-sinB

=sinA+sinB/sinA-sinB

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

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

=tan(A+B)/2.cot(A-B)/2

=R.H.S

Hence sinA+sinB/sinA-sinB=tan(A+B)/2.cot(A+B)/2 is proved

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