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In a triangle ABC, if sin A sin(B-C)=sin...

In a triangle ABC, if `sin A sin(B-C)=sinC sin(A-B)`, then prove that `cos 2A,cos2B` and `cos 2C` are in AP.

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`sinAsin(B-C)=sin(C sin (A-B)`
`rArr sin(B+C)sin(B-C)=sin(A+B)sin(A-B)`
`rArr sin^(2)B-sin^(2)C=sin^(2)A-sin^(2)B`
`rARr 1-cos2B=(1)/(2)(1-cos2A)+(1)/(2)(1-cos2C)`.
`rArr 2cos 2B=cos2A+cos 2C`
Thus, `cos2A,cos 2B,cos 2C` are in AP.
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