求证：sin²A+cos²（A+30）+sinA*cos(A+30)=3/4

求证：sin²A+cos²（A+30）+sinA*cos(A+30)=3/4
求证：sin²A+cos²（A+30）+sinA*cos(A+30)=3/4

求证：sin²A+cos²（A+30）+sinA*cos(A+30)=3/4
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