证明:sinA+sinB+sinC
=2sin[(A+B)/2]cos[(A-B)/2]+sinC
=2cos(C/2)cos[(A-B)/2]+2sin(C/2)cos(C/2)
=2cos(C/2){cos[(A-B)/2]+cos[(A+B)/2]}
=2cos(C/2)[2cos(A/2)cos(B/2)]
=4(cosA/2)(cosB/2)(cosC/2)
根据和差化积,
sinA+sinB+sinC
=2sin[(A+B)/2]cos[(A-B)/2]+sinC
=2cos(C/2)cos[(A-B)/2]+2sin(C/2)cos(C/2)
=2cos(C/2){cos[(A-B)/2]+cos[(A+B)/2]}
=2cos(C/2)[2cos(A/2)cos(B/2)]
=4(cosA/2)(cosB/2)(cosC/2)
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