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Question
Mark the correct alternative in each of the following:
In any ∆ABC, \[a\left( b\cos C - c\cos B \right) =\]
Options
\[a^2\]
\[b^2 - c^2\]
0
\[b^2 + c^2\]
Solution
Using cosine rule, we have
\[a\left( b\cos C - c\cos B \right)\]
\[ = ab\left( \frac{a^2 + b^2 - c^2}{2ab} \right) - ca\left( \frac{c^2 + a^2 - b^2}{2ca} \right)\]
\[ = \frac{a^2 + b^2 - c^2 - c^2 - a^2 + b^2}{2}\]
\[ = \frac{2 b^2 - 2 c^2}{2}\]
\[ = b^2 - c^2\]
Hence, the correct answer is option (b).
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