怎么证明sin^2(a)+cos^2(a+30)+sinacos(a+30)=3/4请告诉我答案及解题过程!谢谢!_数学解答

怎么证明sin^2(a)+cos^2(a+30)+sinacos(a+30)=3/4
请告诉我答案及解题过程!谢谢!

人气：321 ℃　时间：2020-04-22 18:48:42

解答

左边＝(1-cos2α)/2+(1+cos(2α+60°))/2+sinαcos(α+30°)=1+1/2[cos(2α+60°)-cos2α]+1/2[sin(2α+30°)-1/2]=3/4-1/2cos2α+1/2[sin(2α+30°)-sin(2α-30°)]=3/4-1/2cos2α+1/2[2cos2αsin30°]=3/4=右边...