Q68 / 160 · AP EAMCET 2009 · Mathematics

In any $\triangle A B C, a(b \cos C-c \cos B)$ equals

  • A
    $b^2+c^2$
  • Correct answer
    B
    $b^2-c^2$
  • C
    $\frac{1}{b}+\frac{1}{c}$
  • D
    $\frac{1}{b^2}-\frac{1}{c^2}$

Solution

$\begin{aligned} a(b \cos C-c \cos B) & =a b \cos C-a c \cos B \\ & =\frac{a^2+b^2-c^2}{2}-\frac{a^2+c^2-b^2}{2} \\ & =b^2-c^2\end{aligned}$

Hence, the correct answer is option: 'B'.

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