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)

$\left(b^2+c^2\right)a\cos A+\left(c^2+a^2\right)b\cos B+\left(a^2+b^2\right)c\cos C$
$=ab(b\cos A+a\cos B)+bc(b\cos C+c\cos B)+ca(a\cos C+c\cos A)$
$=abc+abc+abc=3abc$