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

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