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

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Prove that: `(sin(A-C)+2sinA+sin(A+C)) / ("sin"("B"-"C")+2sinB+"sin"(B+C))`=`(sinA)/(sinB)``
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`L.H.S. = (sin(A-C)+2sinA+sin(A+C)) / (sin(B-C)+2sinB+sin(B+C))`
`=(sinAcosC-cosAsinC+2sinA+sinAcosC+cosAsinC)/(sinBcosC-cosBsinC+2sinB+sinBcosC+cosBsinC)`
`=(2sinA(1+cosC))/(2sinB(1+cosC))`
`=sinA/sinB = R.H.S.`
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