| 在△ABC中，已知acosB+bcosA=b， （1）求证C=B； （2）若∠ABC的平分线交AC于D，且sin
|
（1）∵acosB+bcosA=b，由正弦定理可得 sinAcosB+cosAsinB=sinB，
∴sin（A+B）=sinB，即sinC=sinB，∴b=c，∴C=B．
（2）△BCD中，用正弦定理可得
=BD DC
，由第一问知道C=B，而BD是角平分线，sinC sin B 2
∴
=2cosBD DC
．C 2
由于三角形内角和为180°，设 A=x，B=2α=C，那么4α+x=180°，故α+
=45°．A 4
∵sin
=A 4
，∴cos3 5
=A 4
，∴cosα=cos（45°-4 5
）=cos45°cosA 4
+sin45°sinA 4
=A 4
．7 2 10
∴
=2cosBD DC
=2cosα=C 2
．7 2 5
| 完形填空。 | |||
| Do you know how to study better and make your study more effective (有效的)?We all know that Chinese students usually study very hard for long 1 .This is very good but it doesn't 2 a lot,for an effective student must have enough sleep,enough food and enough rest and exercise.Every day you need to go out for a walk or visit some friends or some nice places.It's good for your study. When you return to your studies,your mind will be refreshed(清醒) and you'll learn more 3 study better.Psychologists(心理学家) have found that learning takes place this way.Take English learning 4 an example.First you make a lot of progress(进步) and you feel happy.Then your language study seems 5 the same.So you will think you're learning 6 and yo  u may give up.This can last for days or even weeks,yet you needn't give up.At some points your language study will again take another big 7 .You'll see that you really have been learning all along.If you get enough sleep,food,rest and exercise,studying English can be very effective and 8 .Don't give up along the way.Learn slowly and you're sure to get good results. | |||
| ( )1. A. days ( )2. A. help ( )3. A. yet ( )4. A. with ( )5. A. to have ( )6. A. something ( )7. A. work ( )8. A. hard | B. time B. give B. and B. for B. to make B. anything B. jump B. common | C. hours C. make C. or C. as C. to take C. nothing C. walk C. interestin | D. weeks D. take D. but D. to D. to stay D. everything D. result D. possible |