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If b+c=2a then prove that cos(B-C/2)=sinA/2​

Answer»

b+c=2a → 2R \: sinB+2R \: sinC=4R \: sinA \\\\→ sinB+sinC=2sinA \\\\→ 2sin( \frac{b + c}{2} )cos( \frac{b - c}{2} )=4sin \frac{a}{2} \: cos \frac{a}{2} \\\\→ sin( \frac{\pi - a}{2} )cos( \frac{b - c}{2} )=2sin \frac{a}{2} cos \frac{a}{2} \\\\→ cos \frac{a}{2} cos( \frac{b - c}{2} )=2sin \frac{a}{2} cos \frac{a}{2} \\\\→ cos( \frac{b - c}{2} )=2sin \frac{a}{2} \\\\


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