Question

In triangle $ABC , a\left(b^{2}+c^{2}\right) \cos A +b\left(c^{2}+a^{2}\right) \cos B +c\left(a^{2}+b^{2}\right) \cos C$ is equal to

• A. abc
• B. 2abc
• C. 3abc
• D. 4abc

Answer 1

Answer: (C)

$\left(b^{2}+c^{2}\right) a \cos A+\left(c^{2}+a^{2}\right) b \cos B+\left(a^{2}+b^{2}\right) c \cos C$
$=a b(b \cos A+ a \cos B)+b c(b \cos C +c \cos B)+c a(a \cos C +c \cos A)$
$=a b c +a b c +a b c=3 a b c$