2018-2019学年人教B版必修4 3.3三角函数的积化和差与和差化积 作业2
2018-2019学年人教B版必修4 3.3三角函数的积化和差与和差化积 作业2第3页

  =.

  答案:B

  6.解析:cos 20°+cos 60°+cos 100°+cos 140°

  =cos 20°++2cos 120°cos 20°

  =cos 20°+-cos 20°=.

  答案:

  7.解析:sin(α+β)sin(α-β)=(cos 2α-cos 2β)=[(2cos2α-1)-(2cos2β-1)]=cos2β-cos2α=-m.

  答案:-m

  8.解析:y=+sin x=2

  =,

  由已知得,所以<≤1.

  所以y∈.

  答案:

  9.解:

  =

  =

  =8cos 10°sin 20°sin 40°=4(sin 30°+sin 10°)sin 40°

  =2sin 40°+4sin 40°sin 10°

  =2sin 40°-2(cos 50°-cos 30°)=.

  10.解:由题设条件知B=60°,A+C=120°,∴,∴.

  将上式化简为cos A+cos C=cos Acos C,

则=[cos(A+C)+cos(A-C)].