Question

在三角形ABC中，试证明等式，sinA+sinB+sinC=4cosA/2*cosB/2*cosC/2

Answer 1

主要运用了和差化积和半角公式

答案是别人的：
sinA+sinB+sinC
=2sin((A+B)/2)cos((A-B)/2)+2sin(C/2)cos(C/2)
=2sin((π-C)/2)cos((A-B)/2)+2sin(π-(A+B)/2)cos(C/2)
=2cos(C/2)cos((A-B)/2)+2cos((A+B)/2)cos(C/2)
=2cos(C/2)(cos((A-B)/2)+cos((A+B)/2))
=2cos(C/2)2cos(A/2)cos(B/2)
=4cos(A/2)cos(B/2)cos(C/2)

Answer 2

According to Agence France-Presse reported that U.S. Secretary of State on the 3rd Hillary made a speech, calling on Iran to ensure the safety of three missing Americans to return to the United States.
Iran's state-run television station reported that last Saturday, the three Americans from Iraq "infiltration" of Iran and was arrested.
Hillary, the media said: "We are obviously very concerned about the matter. We want this matter to have the results as soon as possible. And we asked the Iranian authorities to help us determine the whereabouts of three missing Americans and their safe return as soon as possible . "