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For any triangle ABC, prove that(b^2-c^2...

For any triangle ABC, prove that`(b^2-c^2)/(a^2)sin2A+(c^2-a^2)/(b^2)sin2B+(a^2-b^2)/(c^2)sin2C=0`

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LHS `=(b^(2)-c^(2))/(a^(2)).(2ka)[(b^(2)+c^(2)-a^(2))/(2bc)]+(c^(2)-a^(2))/(b^(2)) (2kb) [ (a^(2)+c^(2)-b^(2))/(2ac)] + (a^(2)-b^(2))/(c^(2)).2(kc)[(a^(2)+b^(2)-c^(2))/(2ab)]`
`=k/(abc) [(b^(2)-c^(2))(b^(2)+c^(2))-a^(2)(b^(2)-c^(2))+(c^(2)-a^(2))(c^(2)+a^(2))-b^(2)(c^(2)-a^(2))+ (a^(2)+b^(2))(a^(2)-b^(2))-c^(2)(a^(2)-b^(2))]`.
`k/(abc)[b^(4)-c^(4)-a^(2)b^(2)+a^(2)c^(2)+c^(4)-a^(4)-b^(2)c^(2)+a^(2)b^(2)+a^(4)-b^(4)-a^(2)c^(2)+b^(2)c^(2)]=0= RHS`
Hence Proved.
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