Question

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

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

Hint:

Use cosine law and simplify using $a^2+b^2+c^2$ relations.

Answer 1

The Correct Option is C

Step 1: By cosine law, $\cos A = \frac{b^2+c^2-a^2}{2bc}$, etc.}
Step 2: Substitute and simplify to get $3abc$.}