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Distance Formula

In Δ ABC ...

Question

In $Δ$ $A B C$ the sides opposite to angles $A, B, C$ are denoted by $a, b, c$ respectively.
The value of $a [b cos C - c cos B]$ is?

a^{2}

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b^{2}

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0

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b^{2} - c^{2}

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Solution

The correct option is D $b^{2} - c^{2}$
Given: $a [b cos C - c cos B] =$
$= a b cos C - a c cos B$
$= a b \frac{a^{2} + b^{2} - c^{2}}{2 a b} - a c \frac{a^{2} + c^{2} - b^{2}}{2 a c}$ , use cosine rule

$= \frac{a^{2} + b^{2} - c^{2}}{2} - \frac{a^{2} + c^{2} - b^{2}}{2}$
$= b^{2} - c^{2}$

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