求值sin^2A+cos^2(A+30°)+sinAcos(A+30°)
问题描述：
求值sin^2A+cos^2(A+30°)+sinAcos(A+30°)
答
解析：原式=(1-cos2A)/2+[cos(2A+60°)+1]/2
+sinAcos(A+30°)
=1+[cos(2A-60°)-cos2A]/2+sinAcos(A+30°)
=1-sin(2A+30°)/2+sinAcos(A+30°)
=-11/2[sinAcos(A+30°)+cosAsin(A+30°)]+sinAcos(A+30°)
=1+1/2[sinAcos(A+30°)-cosAsin（A+30°)]
=1+1/2*sin[A-(A+30°)]
=1+1/2*sin(-30°)
=1-1/4 =3/4
答
原式=(1-cos2A)/2+[1+cos(2A+60°)]/2+sinAcos(A+30°)=1+(1/2)[cos(2A+60°)-cos2A]+(1/2)sin(2A+30°)-1/4=3/4-1/2cos2A+1/2[sin(2A+30°)-sin(2A-30°)]=3/4-1/2cos2A+1/2[2cos2Asin30°]=3/4