高二数学,三角函数化简两题sin(a+b)cos(y-b)-cos(b+a)sin(b-y)sin(a-b)sin(b-y)-cos(a-b)cos(y-b)

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高二数学,三角函数化简两题sin(a+b)cos(y-b)-cos(b+a)sin(b-y)sin(a-b)sin(b-y)-cos(a-b)cos(y-b)
高二数学,三角函数
化简两题
sin(a+b)cos(y-b)-cos(b+a)sin(b-y)
sin(a-b)sin(b-y)-cos(a-b)cos(y-b)

高二数学,三角函数化简两题sin(a+b)cos(y-b)-cos(b+a)sin(b-y)sin(a-b)sin(b-y)-cos(a-b)cos(y-b)
1、原式=sin(a＋b)cos(y－b)＋cos(a＋b)sin(y－b)
=sin[(a＋b)＋(y－b)]
=sin(a＋y)
2、原式=－[cos(a－b)cos(b－y)－sin(a－b)sin(b－y)]
=－cos[(a－b)＋(b－y)]
=－cos(a－y)

sin(a+b)cos(y-b)-cos(b+a)sin(b-y)
=sin(a+b)cos(b-y)-cos(a+b)sin(b-y)
=sin[(a+b)-(b-y)]
=sin(a+y)
sin(a-b)sin(b-y)-cos(a-b)cos(y-b)
=sin(a-b)sin(b-y)-cos(a-b)cos(b-y)
=-cos[(a-b)+(b-y)]
=-cos(a-y)

sin（a+b)cos(y-b)-cos(b+a)sin(b-y)
=sin（a+b)cos(y-b)+cos(b+a)sin(y-b)
=sin(a+b+y-b)=sin(a+y)
sin(a-b)sin(b-y)-cos(a-b)cos(y-b)
=sin(a-b)sin(b-y)-cos(a-b)cos(b-y)
=cos(a-b+b-y)=cos(a-y)

首先要知道 COS(y-b)=COS[-(b-y)]= COS(b-y)
所以第一个式子用正玄和差化积=sin [(a+b)-(b-y)] =sin (a+y)
第二个式子是余弦和差化积= - [cos(a-b)cos(b-y) - sin(a-b)sin(b-y)]= - cos[a-b+b-y] = - cos(a-y)

1.解原式=sin(a＋b)cos(y－b)＋cos(a＋b)sin(y－b)
=sin[(a＋b)＋(y－b)]
=sin(a＋y)
2、解原式=－[cos(a－b)cos(b－y)－sin(a－b)sin(b－y)]
=－cos[(a－b)＋(b－y)]
=－cos(a－y)

sin(a+b)cos(y-b)-cos(b+a)sin(b-y)
=sin(a+b)cos(y-b)+cos(a+b)sin(y-b)
=sin[(a+b)+(y-b)]
=sin(a+y)
sin(a-b)sin(b-y)-cos(a-b)cos(y-b)
=-[cos(a-b)cos(y-b)-sin(a-b)sin(b-y)]
=-[cos(a-b)cos(b-y)-sin(a-b)sin(b-y)]
=-cos[(a-b)+(b-y)]
=-cos(a-y)

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