First slide

Properties of triangles

Question

In any $∆ A B C$ , the value of $a (b^{2} + c^{2}) \cos A + b (c^{2} + a^{2}) \cos B + c (a^{2} + b^{2}) \cos C =$

Moderate

A

$3 a b c^{2}$
B

$3 a^{2} b c$
C

$3 a b c$
D

$3 a b^{2} c$

Solution

We have,
$\begin{array}{l} a (b^{2} + c^{2}) \cos A + b (c^{2} + a^{2}) \cos B + c (a^{2} + b^{2}) \cos C \\ = a b (b \cos A + a \cos B) + b c (c \cos B + b \cos C) \\ + c a (c \cos A + a \cos C) \\ = a b c + a b c + a b c = 3 a b c \end{array}$

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