Question

In a triangle $ABC$, $(b + c)\cos A + (c + a)\cos B + (a + b)\cos C =$

• A. $2abc$
• B. $abc$
• C. $a + b + c$
• D. $\dfrac{a + b + c}{2abc}$

Hint:

Memorize commonly used geometric identities involving cosine-weighted sums in triangles.

Answer 1

The Correct Option is C

Use identity: In any triangle, the weighted sum identity
$(b + c)\cos A + (c + a)\cos B + (a + b)\cos C = a + b + c$
This is a standard result derived using vector geometry or projection formulae.