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In any DeltaABC, prove that a(bcosC-c ...

In any `DeltaABC`, prove that
`a(bcosC-c cosB)=(b^(2)-c^(2))`

Text Solution

Verified by Experts

L.H.S. = `a(b cos C- c cos B)`
`=a[a((a^(2)+b^(2)-c^(2))/(2ab))-c*((a^(2)+c^(2)-b^(2))/(2ac))]`
`=a((a^(2)+b^(2)-c^(2)-a^(2)-c^(2)+b^(2))/(2a))`
`=(2ab^(2)-2c^(2))/(2)=(2(b^(2)-c^(2)))/(2)`
`=b^(2)-c^(2)=R.H.S`
`:.` L.H.S = R.H.S
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GURUKUL PUBLICATION - MAHARASHTRA PREVIOUS YEAR PAPERS- MARCH 2017-SECTION-II
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