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Prove the identity… (COS B- COS C) / (SIN B +SIN C) =-TAN ((B-C) /2)?
That looks complicated.
It might seem so, but now we can use the double-angle formula for sine, which states that SIN 2X = 2SIN X COS X. When applied to our equation, we get:

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