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If $a = \sin (A - B) \sin (B - C),$ $b = \sin (B - C) \sin (A - C),$ $c = \sin (C - A) s i n (B - C)$ then $a + b + c =$

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Detailed Solution

a = $\sin (A - B) \sin (B - C)$

$b = \sin (B - C) \sin (A - C)$

$c = \sin (C - A) \sin (B - C)$

$2 a + 2 b + 2 c = 2 \sin (A - B) \sin (B - C) + 2 \sin (B - C) \sin (A - C) + 2 \sin (C - A) \sin (B - C)$

$\Rightarrow 2 a + 2 b + 2 c = 0$

$\Rightarrow a + b + c = 0$

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