In ABC prove that a ( b C - c B )= b ^2- c ^2 - Vidyadip

Question

In $\triangle ABC$ prove that $a ( b \cos C - c \cos B )= b ^2- c ^2$

✓

Answer

$ \text { L.H.S. }=a(b \cos C-c \cos B)$
$= a b \cos C-a c \cos B$
$= \frac{1}{2}(2 a b \cos C-2 a c \cos B)$
$= \frac{1}{2}\left\{\left(a^2+b^2-c^2\right)-\left(c^2+a^2-b^2\right)\right\} $
$=\frac{1}{2}\left\{a^2+b^2-c^2-c^2-a^2+b^2\right\}$
$=\frac{1}{2}\left\{2 b^2-2 c^2\right\}$
$=b^2-c^2=\text { R.H.S. }$

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