In ΔABC, write cos $fraction numerator straight B plus straight C over denominator 2 end fraction$ in terms of angle A.

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Solution

cos space fraction numerator straight B plus straight C over denominator 2 end fraction space equals space cos open parentheses fraction numerator 180 degree minus straight A over denominator 2 end fraction close parentheses equals space cos space open parentheses fraction numerator 180 degree over denominator 2 end fraction minus straight A over 2 close parentheses space equals space cos open parentheses 90 degree minus straight A over 2 close parentheses space equals space sin straight A over 2

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