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Prove the identity… (COS B- COS C) / (SIN B +SIN C) =-TAN ((B-C) /2)?
I see. Go on.
Let's start by expressing the left-hand side of the equation in terms of sine and cosine. We have:

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