Q68 / 160 · AP EAMCET 2022 (04 Jul Shift 2) · Mathematics

In any triangle $A B C$ , $(b + c) \cos A + (c + a) \cos B + (a + b) \cos C$ equals

A
$0$
Correct answer
B
$a + b + c$
C
$a + b - c$
D
$a - b - c$

Solution

Given
$(b + c) \cos A + (c + a) \cos B + (a + b) \cos C$
$= (b \cos A + c \cos A) + (c \cos B + a \cos B) + (a \cos C + b \cos C)$
$= (b \cos A + a \cos B) + (c \cos A + a \cos C) + (c \cos B + b \cos C) . . . (1)$
By projection formula, we have
$a = b \cos C + c \cos B$
Therefore, from $(1)$ , we have
$= a + b + c$

Hence, the correct answer is option: 'B'.

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