If $A, B, C$ are the angles of a triangle, show that
$sin B cos (C + A) + cos B sin (C + A) = 0$

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Solution

$A + B + C = π$
$∴ sin B cos (C + A) + cos B sin (C + A)$
$= sin (A + B + C)$
$= sin π = 0$

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