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In any DeltaABC, prove that ac cosB-bc...

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

Text Solution

Verified by Experts

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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GURUKUL PUBLICATION - MAHARASHTRA PREVIOUS YEAR PAPERS- JULY 2018-SECTION II
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