In any triangle ABC,what is the value of a(b | vedclass

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(C) Given expression: $a(b \cos C - c \cos B)$.Using the projection formula or cosine rule:$\cos C = \frac{a^2+b^2-c^2}{2ab}$ and $\cos B = \frac{a^2+

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$b^2-c^2$

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(C) Given expression: $a(b \cos C - c \cos B)$.Using the projection formula or cosine rule:$\cos C = \frac{a^2+b^2-c^2}{2ab}$ and $\cos B = \frac{a^2+c^2-b^2}{2ac}$.Substituting these values into the expression:$a \left( b \left( \frac{a^2+b^2-c^2}{2ab} \right) - c \left( \frac{a^2+c^2-b^2}{2ac} \right) \right)$$= a \left( \frac{a^2+b^2-c^2}{2a} - \frac{a^2+c^2-b^2}{2a} \right)$$= \frac{1}{2} (a^2+b^2-c^2 - a^2 - c^2 + b^2)$$= \frac{1}{2} (2b^2 - 2c^2)$$= b^2 - c^2$.

In any triangle $ABC$,what is the value of $a(b \cos C - c \cos B)$?

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