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Prove that: (sin(B-C))/(cosBcosC)+(sin(C...

Prove that: `(sin(B-C))/(cosBcosC)+(sin(C-A))/(cosCcosA)+(sin(A-B))/(cosAcosB)=0`

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`(a^2sin(B-C))/(sinB+sinC) = ((2RsinA)^2 sin(B-C))/(sinB+sinC)`
`=(4R^2sin^2Asin(B-C))/(sinB+sinC)`
`=(4R^2sinA*sinAsin(B-C))/(sinB+sinC)`
`=(4R^2sinA*sin(pi-(B+C)sin(B-C))/(sinB+sinC)`
`=(4R^2sinA*sin(B+C)sin(B-C))/(sinB+sinC)`
`=(4R^2sinA*(sin^2B-sin^2C))/(sinB+sinC)`
`=(4R^2sinA*(sinB+sinC)(sinB-sinC))/(sinB+sinC)`
`=4R^2sinA(sinB-sinC)`
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