2020-2021学年新教材高中数学第八章向量的数量积与三角恒等变换8.2.4第2课时三角函数的积化和差与和差化积课时分层作业含解析新人教B版必修第三册
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2020-12-19 17:05:27
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课时分层作业课时分层作业(二十二二十二)三角函数的积化和差与和差化积三角函数的积化和差与和差化积(建议用时:40分钟)一、选择题1.cos15°sin105°=()A.34+12B.34-12C.32+1D.32-1A[cos15°sin105°=12[sin(15°+105°)-sin(15°-105°)]=12[sin120°-sin(-90°)]=12×32+12×1=34+12.]2.sin20°+sin40°-sin80°的值为()A.0B.32C.12D.1A[原式=2sin30°cos10°-sin80°=cos10°-sin80°=sin80°-sin80°=0.]3.函数f(x)=2sinx2sinα-x2的最大值等于()A.2sin2α2B.-2sin2α2C.2cos2α2D.-2cos2α2A[f(x)=2sinx2sinα-x2=-[cosα-cos(x-α)]=cos(x-α)-cosα.当cos(x-α)=1时,f(x)取得最大值1-cosα=2sin2α2.]4.将cos2x-sin2y化为积的形式,结果是()A.-sin(x+y)sin(x-y)B.cos(x+y)cos(x-y)C.sin(x+y)cos(x-y)D.-cos(x+y)sin(x-y)B[cos2x-sin2y=1+cos2x2-1-cos2y2=12(cos2x+cos2y)=cos(x+y)cos(x-y).]5.若cosxcosy+sinxsiny=12,sin2x+sin2y=23,则sin(x+y)=()A.23B.-23
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