Question:
In a triangle $ABC$, $(b + c)\cos A + (c + a)\cos B + (a + b)\cos C =$
In a triangle $ABC$, $(b + c)\cos A + (c + a)\cos B + (a + b)\cos C =$
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Memorize commonly used geometric identities involving cosine-weighted sums in triangles.
Updated On: May 19, 2025
- $2abc$
- $abc$
- $a + b + c$
- $\dfrac{a + b + c}{2abc}$
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The Correct Option is C
Solution and Explanation
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.
$(b + c)\cos A + (c + a)\cos B + (a + b)\cos C = a + b + c$
This is a standard result derived using vector geometry or projection formulae.
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