The conversation between human and AI assistant.
Prove the identity… (COS B- COS C) / (SIN B +SIN C) =-TAN ((B-C) /2)?
So, how does this simplify to the right-hand side of the equation?
After some simplification, we get:

[COS B - COS C] / [SIN (B-C) COS (B-C)+SIN(B-C)]
= [(COS B - COS C)/ SIN (B-C)] / [(COS (B-C) + 1)/ SIN (B-C)]
= -TAN ((B-C) /2)