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§¢§©§¥ 79-§â §Ò?§â§ï§ß §Õ§å§ß§Õ §ã§å§â§Ô§å§å§Ý§î §®§Ñ§ä§Ö§Þ§Ñ§ä§Ú§Ü-10 §·§Ú§é§ï§ï§Ý§Õ§ï§ï §à§â§è§Ô§à§à§×!
§®§Ñ§ä§Ö§Þ§Ñ§ä§Ú§Ü10 §´§â§Ú§Ô§à§ß§à§Þ§Ö§ä§â §æ§å§ß§Ü§è??§Õ§í§ß §ß§Ú§Û§Ý§Ò§ï§â, §ñ§Ý§Ô§Ñ§Ó§Ñ§â§í§ß §ä§à§Þ§ì§×§à sin( ¦Á+¦Â)=sin¦Á ¡¤ cos¦Â+cos¦Á ¡¤ sin¦Â §´§â§Ú§Ô§à§ß§à§Þ§Ö§ä§â §æ§å§ß§Ü§è§Ú§Û§ß §ß§Ú§Û§Ý§Ò§ï§â, §ñ§Ý§Ô§Ñ§Ó§Ñ§â§í§Ô §ç§ñ§Ý§Ò§Ñ§â §Ñ§â§Ô§Ñ§Ñ§â §Ò§à§Õ§à§Ø §ã§å§â§Ñ§ç §´§â§Ú§Ô§à§ß§à§Þ§Ö§ä§â §æ§å§ß§Ü§è§Ú§Û§ß ?§ß§è§Ô§Ú§Û§Ô §Ñ§ê§Ú§Ô§Ý§Ñ§ß §ç§ñ§Ý§Ò§Ñ§â §ä§â§Ú§Ô§à§ß§à§Þ§Ö§ä§â §æ§å§ß§Ü§è§ï§Õ §ê?§Ý§Ø??§Ý§ï§ß §Ò§à§Õ§à§ç §·§ï§â§ï§Ô§Ý§ï§Ô§Õ§ï§ç??§ß sin( ¦Á-¦Â)=sin¦Á ¡¤ cos¦Â-cos¦Á ¡¤ sin¦Â cos( ¦Á+¦Â)=cos¦Á ¡¤ cos¦Â-sin¦Á ¡¤ sin¦Â cos( ¦Á-¦Â)=cos¦Á ¡¤ cos¦Â+sin¦Á ¡¤ sin¦Â
§´§â§Ú§Ô§à§ß§à§Þ§Ö§ä§â §æ§å§ß§Ü§è§Ú§Û§ß ?§â§Ô§ï§Ý§Ø §Õ§Ñ§Û§â§Ñ§Ý§Õ§Õ§Ñ§Ô ?§ß§è§Ô§Ú§Û§ß §å§ä§Ô§å§å§Õ. YOUR SUBTOPICS GO HERE §¯??§â
sin ¦Á + sin ¦Â =? ¦Á=x+y ¦Â =x-y §Ô§ï§Ø §à§â§Ý§å§å§Ý§ì§ñ, §´§ï§Ô§Ó§ï§Ý sin ¦Á +sin ¦Â =sin (x+y) +sin (x-y)= sinxcos y +cos x siny+sin xcosy-cosxsiny=2 sinxcos y x+y=¦Á x-y=¦Â §ï§ß§ï 2 §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý§Ú§Û§Ô §ß§ï§Þ§Ò§ï§Ý x=(¦Á+¦Â)/2 §Ò§à§Ý§ß§à.??§ß§ï§ï§ã y=(¦Á-¦Â)/2 §Ô§ï§Ø §Ô§Ñ§â§ß§Ñ.?§Þ§ß?§ç §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý§Õ§ï§ï §à§â§Ý§å§å§Ý§Ò§Ñ§Ý: sin ¦Á +sin ¦Â=2 sinxcos y=2 sin (¦Á+¦Â)/2 cos (¦Á-¦Â)/2 sin ¦Á +sin ¦Â=2 sin (¦Á+¦Â)/2 cos (¦Á-¦Â)/2 (1) §¢?§Ô§Õ§ï§ï§â§ï§ï §¿§ß§ï §ß§Ú§Û§Ý§Ò§ï§â §Á§Þ§Ñ§â §Ô§Ñ§â§Ñ§ç§í§Ô §ã§à§ß§Ú§â§ç§à§× §¥§Ñ§â§Ñ§Ñ§ç
sin ¦Á- sin ¦Â =? sin ¦Á- sin ¦Â =sin (x+y)- sin (x-y)= sinxcos y +cos x siny-sin xcosy+cosxsiny= = 2cos xsin y sin ¦Á- sin ¦Â= 2cos xsin y= 2C os (¦Á+¦Â)/2 Sin (¦Á-¦Â)/2 sin ¦Á- sin ¦Â=2C os (¦Á+¦Â)/2 Sin (¦Á-¦Â)/2 (2) §®?§ß §Ñ§Õ§Ú§Ý§Ñ§Ñ§â §ñ§Ý§Ô§Ñ§Ó§â§í§ß §ä§à§Þ§ì§×§à§Ô §Ô§Ñ§â§Ô§Ñ§ñ. §¥§Ñ§â§Ñ§Ñ§ç
§®?§ß §Ñ§Õ§Ú§Ý§Ñ§Ñ§â cos-§í§ß §ä§à§Þ§ì§×§à§Ô §Ô§Ñ§â§Ô§Ñ§ß§Ñ §å§å? cos ¦Á+ cos ¦Â=2C os (¦Á+¦Â)/2 Cos (¦Á-¦Â)/2 (3) Cos¦Á-Cos¦Â=2sin(¦Á+¦Â)/2Sin(¦Â-¦Á)/2 (4) §¥§Ñ§â§Ñ§Ñ§ç
tg ¦Á +tg ¦Â =Sin( ¦Á + ¦Â )/Cos ¦Á Cos ¦Â (5) tg ¦Á- tg ¦Â =Sin( ¦Á - ¦Â )/Cos ¦Á Cos ¦Â (6) ctg¦Á+c tg ¦Â= Sin( ¦Á + ¦Â )/Sin ¦Á Sin ¦Â (7) ctg¦Á-c tg ¦Â= Sin( ¦Á - ¦Â )/Sin ¦Á Sin ¦Â (8) §¯§ï§Þ§ï§Ý§ä §ä§à§Þ§ì§×§à§ß§å§å§Õ §¥§Ñ§â§Ñ§Ñ§ç
§¨§Ú§ê§ï§ï §Ò§à§Õ§Ý§à§Ô§à ¡í1 Sin10 ¡ã +sin50 ¡ã §¯§Ú§Û§Ý§Ò§ï§â§Ú§Û§Ô §ç§ñ§Ý§Ò§Ñ§â§é§Ú§Ý Sin10 ¡ã +sin50 ¡ã = =2sin(10 ¡ã+50¡ã)/2 ¡¤ Cos( 10 ¡ã-50¡ã)/2= =2sin30 ¡ã Cos20 ¡ã= =2¡¤1/2¡¤Cos20¡ã= = Cos20¡ã ; §¥§Ñ§â§Ñ§Ñ§ç
§¨§Ú§ê§ï§ï §Ò§à§Õ§Ý§à§Ô§à ¡í2 §·§ñ§Ý§Ò§Ñ§â§é§Ú§Ý Cos( ¦Á + ¦Â ) ¡¤ Cos( ¦Á - ¦Â )-Sin( ¦Á + ¦Â ) ¡¤Sin ( ¦Á - ¦Â )=? Cos( ¦Á + ¦Â ) ¡¤ Cos( ¦Á - ¦Â )-Sin( ¦Á + ¦Â ) ¡¤Sin ( ¦Á - ¦Â )= =Cos( ¦Á + ¦Â+¦Á - ¦Â )= =Cos2 ¦Á ; §·??§ç§Õ??§Õ§ï§ï §ñ§Þ§Ñ§â §´§à§Þ§î§×§à §Õ§Ñ§ß §Ü§à§ã§Ú§ß§å§ã, §³§Ú§ß§å§ã§Ñ§Ñ§â §Ù§Ñ§Õ§Ñ§â§Õ§Ñ§Ô §Ò§Ú§Ý§ï§ï, §ã§Ñ§ß§Ñ§è§Ô§Ñ§Ñ§ñ! §¥§Ñ§â§Ñ§Ñ§ç
§¢§à§Õ§à§è§Ô§à§à§×! sin(150 ¡ã )=?
cos(225 ¡ã )=?
sin2 ¦Á =?

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800.mn 2006 §®§Ñ§ä§Ö§Þ§Ñ§ä§Ú§Ü§Ú§Û§ß §ç§Ú§é§ï§ï§Ý§Ú§Û§ß §ä§Ö§ã§ä §Ò§Ñ §ä?§Ý§ç??§â by byambaa avirmed
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tungaa53
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800.mn - 2010 §®§Ñ§ä§Ö§Þ§Ñ§ä§Ú§Ü §¿§¦§º by byambaa avirmed
800.mn - 2010 §®§Ñ§ä§Ö§Þ§Ñ§ä§Ú§Ü §¿§¦§º by byambaa avirmed800.mn - 2010 §®§Ñ§ä§Ö§Þ§Ñ§ä§Ú§Ü §¿§¦§º by byambaa avirmed
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800.mn - 2007 §®§Ñ§ä§Ö§Þ§Ñ§ä§Ú§Ü §¿§¦§º by byambaa avirmed
800.mn - 2007 §®§Ñ§ä§Ö§Þ§Ñ§ä§Ú§Ü §¿§¦§º by byambaa avirmed800.mn - 2007 §®§Ñ§ä§Ö§Þ§Ñ§ä§Ú§Ü §¿§¦§º by byambaa avirmed
800.mn - 2007 §®§Ñ§ä§Ö§Þ§Ñ§ä§Ú§Ü §¿§¦§º by byambaa avirmed
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Tsahim.le3

  • 1. §¢§©§¥ 79-§â §Ò?§â§ï§ß §Õ§å§ß§Õ §ã§å§â§Ô§å§å§Ý§î §®§Ñ§ä§Ö§Þ§Ñ§ä§Ú§Ü-10 §·§Ú§é§ï§ï§Ý§Õ§ï§ï §à§â§è§Ô§à§à§×!
  • 2. §®§Ñ§ä§Ö§Þ§Ñ§ä§Ú§Ü10 §´§â§Ú§Ô§à§ß§à§Þ§Ö§ä§â §æ§å§ß§Ü§è??§Õ§í§ß §ß§Ú§Û§Ý§Ò§ï§â, §ñ§Ý§Ô§Ñ§Ó§Ñ§â§í§ß §ä§à§Þ§ì§×§à sin( ¦Á+¦Â)=sin¦Á ¡¤ cos¦Â+cos¦Á ¡¤ sin¦Â §´§â§Ú§Ô§à§ß§à§Þ§Ö§ä§â §æ§å§ß§Ü§è§Ú§Û§ß §ß§Ú§Û§Ý§Ò§ï§â, §ñ§Ý§Ô§Ñ§Ó§Ñ§â§í§Ô §ç§ñ§Ý§Ò§Ñ§â §Ñ§â§Ô§Ñ§Ñ§â §Ò§à§Õ§à§Ø §ã§å§â§Ñ§ç §´§â§Ú§Ô§à§ß§à§Þ§Ö§ä§â §æ§å§ß§Ü§è§Ú§Û§ß ?§ß§è§Ô§Ú§Û§Ô §Ñ§ê§Ú§Ô§Ý§Ñ§ß §ç§ñ§Ý§Ò§Ñ§â §ä§â§Ú§Ô§à§ß§à§Þ§Ö§ä§â §æ§å§ß§Ü§è§ï§Õ §ê?§Ý§Ø??§Ý§ï§ß §Ò§à§Õ§à§ç §·§ï§â§ï§Ô§Ý§ï§Ô§Õ§ï§ç??§ß sin( ¦Á-¦Â)=sin¦Á ¡¤ cos¦Â-cos¦Á ¡¤ sin¦Â cos( ¦Á+¦Â)=cos¦Á ¡¤ cos¦Â-sin¦Á ¡¤ sin¦Â cos( ¦Á-¦Â)=cos¦Á ¡¤ cos¦Â+sin¦Á ¡¤ sin¦Â
  • 3. §´§â§Ú§Ô§à§ß§à§Þ§Ö§ä§â §æ§å§ß§Ü§è§Ú§Û§ß ?§â§Ô§ï§Ý§Ø §Õ§Ñ§Û§â§Ñ§Ý§Õ§Õ§Ñ§Ô ?§ß§è§Ô§Ú§Û§ß §å§ä§Ô§å§å§Õ. YOUR SUBTOPICS GO HERE §¯??§â
  • 4. sin ¦Á + sin ¦Â =? ¦Á=x+y ¦Â =x-y §Ô§ï§Ø §à§â§Ý§å§å§Ý§ì§ñ, §´§ï§Ô§Ó§ï§Ý sin ¦Á +sin ¦Â =sin (x+y) +sin (x-y)= sinxcos y +cos x siny+sin xcosy-cosxsiny=2 sinxcos y x+y=¦Á x-y=¦Â §ï§ß§ï 2 §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý§Ú§Û§Ô §ß§ï§Þ§Ò§ï§Ý x=(¦Á+¦Â)/2 §Ò§à§Ý§ß§à.??§ß§ï§ï§ã y=(¦Á-¦Â)/2 §Ô§ï§Ø §Ô§Ñ§â§ß§Ñ.?§Þ§ß?§ç §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý§Õ§ï§ï §à§â§Ý§å§å§Ý§Ò§Ñ§Ý: sin ¦Á +sin ¦Â=2 sinxcos y=2 sin (¦Á+¦Â)/2 cos (¦Á-¦Â)/2 sin ¦Á +sin ¦Â=2 sin (¦Á+¦Â)/2 cos (¦Á-¦Â)/2 (1) §¢?§Ô§Õ§ï§ï§â§ï§ï §¿§ß§ï §ß§Ú§Û§Ý§Ò§ï§â §Á§Þ§Ñ§â §Ô§Ñ§â§Ñ§ç§í§Ô §ã§à§ß§Ú§â§ç§à§× §¥§Ñ§â§Ñ§Ñ§ç
  • 5. sin ¦Á- sin ¦Â =? sin ¦Á- sin ¦Â =sin (x+y)- sin (x-y)= sinxcos y +cos x siny-sin xcosy+cosxsiny= = 2cos xsin y sin ¦Á- sin ¦Â= 2cos xsin y= 2C os (¦Á+¦Â)/2 Sin (¦Á-¦Â)/2 sin ¦Á- sin ¦Â=2C os (¦Á+¦Â)/2 Sin (¦Á-¦Â)/2 (2) §®?§ß §Ñ§Õ§Ú§Ý§Ñ§Ñ§â §ñ§Ý§Ô§Ñ§Ó§â§í§ß §ä§à§Þ§ì§×§à§Ô §Ô§Ñ§â§Ô§Ñ§ñ. §¥§Ñ§â§Ñ§Ñ§ç
  • 6. §®?§ß §Ñ§Õ§Ú§Ý§Ñ§Ñ§â cos-§í§ß §ä§à§Þ§ì§×§à§Ô §Ô§Ñ§â§Ô§Ñ§ß§Ñ §å§å? cos ¦Á+ cos ¦Â=2C os (¦Á+¦Â)/2 Cos (¦Á-¦Â)/2 (3) Cos¦Á-Cos¦Â=2sin(¦Á+¦Â)/2Sin(¦Â-¦Á)/2 (4) §¥§Ñ§â§Ñ§Ñ§ç
  • 7. tg ¦Á +tg ¦Â =Sin( ¦Á + ¦Â )/Cos ¦Á Cos ¦Â (5) tg ¦Á- tg ¦Â =Sin( ¦Á - ¦Â )/Cos ¦Á Cos ¦Â (6) ctg¦Á+c tg ¦Â= Sin( ¦Á + ¦Â )/Sin ¦Á Sin ¦Â (7) ctg¦Á-c tg ¦Â= Sin( ¦Á - ¦Â )/Sin ¦Á Sin ¦Â (8) §¯§ï§Þ§ï§Ý§ä §ä§à§Þ§ì§×§à§ß§å§å§Õ §¥§Ñ§â§Ñ§Ñ§ç
  • 8. §¨§Ú§ê§ï§ï §Ò§à§Õ§Ý§à§Ô§à ¡í1 Sin10 ¡ã +sin50 ¡ã §¯§Ú§Û§Ý§Ò§ï§â§Ú§Û§Ô §ç§ñ§Ý§Ò§Ñ§â§é§Ú§Ý Sin10 ¡ã +sin50 ¡ã = =2sin(10 ¡ã+50¡ã)/2 ¡¤ Cos( 10 ¡ã-50¡ã)/2= =2sin30 ¡ã Cos20 ¡ã= =2¡¤1/2¡¤Cos20¡ã= = Cos20¡ã ; §¥§Ñ§â§Ñ§Ñ§ç
  • 9. §¨§Ú§ê§ï§ï §Ò§à§Õ§Ý§à§Ô§à ¡í2 §·§ñ§Ý§Ò§Ñ§â§é§Ú§Ý Cos( ¦Á + ¦Â ) ¡¤ Cos( ¦Á - ¦Â )-Sin( ¦Á + ¦Â ) ¡¤Sin ( ¦Á - ¦Â )=? Cos( ¦Á + ¦Â ) ¡¤ Cos( ¦Á - ¦Â )-Sin( ¦Á + ¦Â ) ¡¤Sin ( ¦Á - ¦Â )= =Cos( ¦Á + ¦Â+¦Á - ¦Â )= =Cos2 ¦Á ; §·??§ç§Õ??§Õ§ï§ï §ñ§Þ§Ñ§â §´§à§Þ§î§×§à §Õ§Ñ§ß §Ü§à§ã§Ú§ß§å§ã, §³§Ú§ß§å§ã§Ñ§Ñ§â §Ù§Ñ§Õ§Ñ§â§Õ§Ñ§Ô §Ò§Ú§Ý§ï§ï, §ã§Ñ§ß§Ñ§è§Ô§Ñ§Ñ§ñ! §¥§Ñ§â§Ñ§Ñ§ç
  • 13. sin(45 ¡ã +x) ¡¤ cos (x-45 ¡ã )-cos(45 ¡ã +x) ¡¤sin (x-45 ¡ã )=?
  • 14. sin(30 ¡ã +x) ¡¤ cosx - cos(30 ¡ã+x ) ¡¤ sinx=?
  • 15. cos(60 ¡ã +x) ¡¤ cosx + sin(60 ¡ã+x ) ¡¤ sinx=? sin, cos, tg, ctg??? §¥§Ñ§â§Ñ§Ñ§ç
  • 16. §¤§ï§â§Ú§Û§ß §Õ§Ñ§Ñ§Ý§Ô§Ñ§Ó§Ñ§â §³§å§â§Ô§Ñ§Ý§ä§í§ß §Þ§Ñ§ä§Ö§â§Ú§Ñ§Ý§í§ß §ç§å§å§Õ§Ñ§ã-42
  • 17. ¡í 1-20 §ç?§â§ä§ï§Ý§ç §Ò§à§Õ§Ý§à§Ô§à
  • 18. §³§å§â§Ñ§ç §Ò§Ú§é§Ú§Ô §ç§å§å§Õ§Ñ§ã-92, ¡í 480-490 §·??§ç§Õ??§Õ§ï§ï §Ô§ï§â§Ú§Û§ß §Õ§Ñ§Ñ§Ý§Ô§Ñ§Ó§Ñ§â§Ñ§Ñ §Ò§Ú§é§ï§ï§Õ §Ñ§Ó§Ñ§Ñ§â§Ñ§Û... §¥§Ñ§â§Ñ§Ñ§ç
  • 19. §Á.§¯§Ñ§ß§Õ§Ú§ß§è§ï§è§ï§Ô §·§Ú§é§ï§ï§Ý§Õ§ï§ï §Ú§Õ§ï§Ó§ç§Ú§ä§ï§Û §à§â§à§Ý§è§ã§à§ß §ä§Ñ §Ò?§ç§ï§ß§Õ§ï§ï §Ò§Ñ§ñ§â§Ý§Ñ§Ý§Ñ§Ñ. §¯??§â
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