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Prove that: (sin(A-C)+2sinA+sin(A+C))/...

Prove that:
`(sin(A-C)+2sinA+sin(A+C))/(sin(B-C)+2sinB+sin(B+C))=(sinA)/(sinB)`

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To prove the equation \[ \frac{\sin(A-C) + 2\sin A + \sin(A+C)}{\sin(B-C) + 2\sin B + \sin(B+C)} = \frac{\sin A}{\sin B}, \] we will simplify the left-hand side (LHS) step by step. ...
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