1
Question
a(sin B−sin C)+b(sin C−sin A)+c(sin A−sin B)=0
a(sin B−sin C)+b(sin C−sin A)+c(sin A−sin B)=0
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Solution
LHS,a(sin B − sin C)+b(sin C − sin A)+c(sin A − sin B)=a sin B − a sin C+b sin C−b sin A+c sin A−c sin B=b sin A−c sin A+c sin B−b sin A+c sin A−c sin B[∵ b sin A = a sin B, b sin C = c sin B, c sin A = a sin C]=0=RHSHence proved.
LHS,a(sin B − sin C)+b(sin C − sin A)+c(sin A − sin B)=a sin B − a sin C+b sin C−b sin A+c sin A−c sin B=b sin A−c sin A+c sin B−b sin A+c sin A−c sin B[∵ b sin A = a sin B, b sin C = c sin B, c sin A = a sin C]=0=RHSHence proved.
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