2019-2020学年新教材人教B版第三册课时分层作业：三角函数的积化和差与和差化积.doc

教学资料范本2019-2020学年新教材人教B版第三册课时分层作业：三角函数的积化和差与和差化积编 辑：_时 间：_(建议用时：60分钟)合格基础练一、选择题1.cos 15 sin 105()ABC1 D1Acos 15sin 105 sin(15105)sin(15105) sin 120sin(90) 1 .2.sin 20sin 40sin 80的值为()A0BCD1A原式2sin 30cos 10sin 80cos 10sin 80sin 80sin 800.3.函数f(x)2sin sin的最大值等于()A2sin2B2sin2 C2cos 2D2cos 2 Af(x)2sin sincos cos(x)cos(x)cos .当cos(x)1时.f(x)取得最大值1cos 2sin2 .4将cos 2xsin2y化为积的形式.结果是()Asin(xy)sin(xy)Bcos(xy)cos(xy)Csin(xy)cos(xy)Dcos(xy)sin(xy)Bcos2xsin2y(cos 2xcos 2y)cos(xy)cos(xy)5若cos xcos ysin xsin y.sin 2xsin 2y.则sin(xy)()AB C .DAcos xcos ysin xsin y.cos.sin 2xsin 2y.2sincos.2sin.sin(xy).故选A二、填空题6cos 2cos 3化为积的形式为_2sin sincos 2cos 32sin sin2sin sin2sin sin . 7sincos 化为和差的结果是_ cos() sin()原式sinsin() cos() sin()8._.原式 .三、解答题9求下列各式的值：(1)sin 54sin 18；(2)cos 146cos 942cos 47cos 73.解(1)sin 54sin 182cos 36sin 182 .(2)cos 146cos 942cos 47cos 732cos 120cos 262(cos 120cos 26)2cos 26cos 26cos 26cos 26 .10在ABC中.若B30.求cos Asin C的取值范围解由题意.得cos Asin Csin(AC)sin(AC)sin(B)sin(AC)sin(AC)B30.150AC150.1sin(AC)1.sin(AC).cos Asin C的取值范围是.等级过关练1.cos 40cos 60cos 80cos 160()AB CDAcos 60cos 80cos 40cos 160cos 802cos 100cos 60cos 80cos 80 .2.已知.且cos cos .则cos()_.A B CDAcos cos 2cos cos 2cos cos cos .cos()2cos 2121.3.函数ycoscos的最大值是_由题意知.y(cos 2xcos )cos 2x.因为1cos 2x1.所以ymax.4._.2cos 30.5已知f(x).x(0.)(1)将f(x)表示成cos x的多项式；(2)求f(x)的最小值解(1)f(x)2co