Question

Let ( a / sin A=b / sin B=c / sin C=k )
Then, ( a=k sin A, b=k sin B, c=k sin C )
( mathrm{RHS} )
( mathrm{b}-mathrm{c} / mathrm{a} cos mathrm{A} / 2 )
( =(k sin B-k sin C / k sin A) cos A / 2 )
( ={[2 cos B+C / 2 sin B-C / 2] / sin A} cos A / 2 )
( =left[2^{star} sin B-C / 2 cos (p i / 2-A / 2) cdot cos A / 2right] / sin A )
( =left[sin A^{*} sin B-C / 2right] / sin A )
( =sin B-C / 2 )
( =mathrm{LHS} )

# - с -COS 7. For any triangle ABC, prove that s if ZB = 60

Solution