In any triangle $\mathrm{ABC}, a(b \cos C-c \cos B)=$

In any triangle $\mathrm{ABC}, a(b \cos C-c \cos B)=$
  1. $b-c$
  2. $b+c$
  3. $b^2-c^2$
  4. $b^2+c^2$

Solution

Given expression a (bcosc $-\cos B)$. $ \begin{aligned} & a b \cos C-a c c o s B=a b \frac{\left(a^2+b^2-c^2\right)}{2 a b}-a c \frac{\left(a^2+c^2-b^2\right)}{2 a c} \\ & =\frac{1}{2}\left[a^2+b^2-c^2-a^2-c^2+b^2\right] \\ & =\frac{1}{2}\left[2\left(b^2-c^2\right)\right]=b^2-c^2 \end{aligned} $

Asked in: AP EAMCET 2022 (06 Jul Shift 1)

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