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Prove the identity… (COS B- COS C) / (SIN B +SIN C) =-TAN ((B-C) /2)?
And the last step is to simplify, right?
Yes, we can use the half-angle formula for tangent, which states that TAN (X/2) = SIN X / (1 + COS X). In our case, we replace X with (B-C):

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