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If in a A B C ,(sinA)/(sinC)=(sin(A-B))...

If in a ` A B C ,(sinA)/(sinC)=(sin(A-B))/(sin(B-C)` , prove that `a^2,b^2,c^2` are in `AdotPdot`

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Given, `(sinA sin(B - C))/(sinC sin(A - B)) = 1 `
`L.H.S = (sin(B + C)sin(B - C))/(sin(A + B)sin(A - B) `
= `(cos2B - cos2C)/(cos2A - cos2B) = 1 `
=`2 cos 2B=cos 2A+cos 2C`
=`2(1-2sin^2B)=(1-2sin^2A)+(1-2sin^2C)`
⇒` 2sin^2B = sin^2A + sin^2C `
⇒ `2b^2 = a^2 + c^2 `
...
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