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Question

If b+c=2a, then prove that that cos(BC2)=2sinA2.

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Solution

Given b+c=2a
2RsinB+2RsinC=4RsinA
sinB+sinC=2sinA
2sin(B+C2)cos(BC2)=4sinA2cosA2
sin(πA2)cos(BC2)=2sinA2cosA2
cosA2cos(BC2)=2sinA2cosA2
cos(BC2)=2sinA2

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