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Question

In ABC prove that sin(BC2)=(bc2) cosA2.

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Solution

ABC is a triangle.

A+B+C=π

sinAa=sinBb=sinCc=k

2cos(B+C2)sin(BC2)=(bc)k

2sin(A2)sin(BC2)=(bc)k

sinA=ak

2sinA2cosA2=ak

sin(BC2)cos(A2)=(bca)

sin(BC2)=(bca)cos(A2)

Hence Proved

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