1.化简sin 2α-2sin2α+1的结果可以是 ( )
A.2sin(2α+30°) B.2sin(2α-30°)
C.2sin(2α+60°) D.2sin(2α-60°)
【解析】选A. sin 2α-2sin2α+1= sin 2α+cos 2α
=2
=2(sin 2αcos 30°+cos 2αsin 30°)=2sin(2α+30°).
2.由1+2cos(2x-60°)和化积为 ( )
A.2cos(x-60°)cos x B.2sin(x-60°)sin x
C.4cos(x-60°)cos x D.4cos(x-60°)sin x
【解析】选C.由和差化积公式,得1+2cos(2x-60°)
=2
=2[cos 60°+cos(2x-60°)]=4cos xcos(x-60°).
3.化简4sin(x+30°)cos x= ( )
A.sin(2x+30°)+1 B.sin(2x+30°)-1
C.2sin(2x+30°)+1 D.2cos(2x+30°)+1
【解析】选C.由积化和差公式,得4sin(x+30°)cos x
=2[sin(2x+30°)+sin 30°]=2sin(2x+30°)+1.
