1.

In any `DeltaABC`, prove that `ac cosB-bc cosA=(a^(2)-b^(2))`

Answer» L.H.S. `=ac""cosB-bc""cosA`
`=ac((a^(2)+c^(2)-b^(2))/(2ac))-bc((b^(2)+c^(2)-a^(2))/(2bc))" "` [by cosine rule]
`=(1)/(2)[a^(2)+c^(2)-b^(2)-b^(2)-c^(2)+a^(2)]`
`=(1)/(2)[2a^(2)-2b^(2)]`
`=(1)/(2)xx2(a^(2)-b^(2))=a^(2)-b^(2)=R.H.S.
`:.L.H.S.=R.H.S.`


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