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Some Applications Of Trigonometry

Question

If A, B, C are the interior angles of a triangle ABC then $sin space open parentheses fraction numerator straight B plus straight C over denominator 2 end fraction close parentheses$ is equal to
$cos space straight B over 2$
$cos space straight C over 2$
$cos space straight A over 2$

none of these

Solution

cos space straight A over 2