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Problem In a Δ A B C \Delta ABC Δ A B C ( b + c ) cos A 2 = a sin ( B + C 2 ) (b+c) \cos \frac{A}{2} = a \sin \left( \frac{B+C}{2} \right) ( b + c ) cos 2 A = a sin ( 2 B + C ) ( b + c ) cos ( B + C 2 ) = a sin A 2 (b+c) \cos \left( \frac{B+C}{2} \right) = a \sin \frac{A}{2} ( b + c ) cos ( 2 B + C ) = a sin 2 A ( b − c ) cos ( B − C 2 ) = a cos ( A 2 ) (b-c) \cos \left( \frac{B-C}{2} \right) = a \cos \left( \frac{A}{2} \right) ( b − c ) cos ( 2 B − C ) = a cos ( 2 A ) ( b − c ) cos A 2 = a sin ( B − C 2 ) (b-c) \cos \frac{A}{2} = a \sin \left( \frac{B-C}{2} \right) ( b − c ) cos 2 A = a sin ( 2 B − C ) Browse the problem library