# Mark the correct alternative in each of the following:

Question:

Mark the correct alternative in each of the following:

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

(a) $a^{2}$

(b) $b^{2}-c^{2}$

(c) 0

(d) $b^{2}+c^{2}$

Solution:

Using cosine rule, we have

$a(b \cos C-c \cos B)$

$=a b\left(\frac{a^{2}+b^{2}-c^{2}}{2 a b}\right)-c a\left(\frac{c^{2}+a^{2}-b^{2}}{2 c a}\right)$

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

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

$=b^{2}-c^{2}$

Hence, the correct answer is option (b).