5.5.1.1 两角差的余弦公式课堂检测素养达标1.cos 20=()A.cos 30cos 10-sin 30sin 10B.cos 30cos 10+sin 30sin 10C.sin 30cos 10-sin 10cos 30D.cos 30cos 10-sin 30cos 10【解析】选B.cos 20=cos(30-10)=cos 30cos 10+sin 30sin 10.2.cos (-35)cos (25+)+sin (-35)sin (25+)的值为()A.-B.C.-D.【解析】选B.原式=cos (-35)-(+25)=cos 60=.3.已知sin =,则sin=_.【解析】由sin =,得cos =-=-.所以sin=cos=cos=cos +sin =.答案:4.已知sin +sin +sin =0,cos +cos +cos =0,求证:cos(-)=-.【证明】由sin +sin +sin =0,cos +cos +cos =0得(sin +sin )2=(-sin )2,(cos +cos )2=(-cos )2.+得,2+2(cos cos +sin sin )=1,即2+2cos(-)=1,所以cos(-)=-.1