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Question

Prove:
a(cosB+cosC)=2(b+c)sin2A2

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Solution

Given that,
a(cosB+cosC)=2(b+c)sin2A2R.H.S=2(b+c)sin2A2=2k(sinB+sinc).sin2A2=2k2sin(B+C2).cos(BC2)sin2A2=4k.sin(B+C2).cos(BC2).cos2(B+C2)=2k.2sin(B+C2).cos(BC2).cos(BC2).cos(B+C2)=ksin(B+C).(cosB+cosC)=ksinA(cosB+cosC)=a(cosB+cosC)=L.H.Sproved.

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