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Консультация № 183123
11.05.2011, 11:24
43.95 руб.
0
3
1
Здравствуйте! Прошу помощи в следующем вопросе:Докажите неравенство P>4R,где P-периметр,а R-радиус описанной окружности остроугольного треугольника.Заранее благодарен.
Обсуждение
11.05.2011, 13:01
общий
это ответ
Здравствуйте, Тимофеев Алексей Валентинович!
Воспользуемся формулой
Отсюда
Суммируя по всем сторонам треугольника
Пытаемся доказать, что
, при условии, что 
Пусть [$945$] - наименьший угол. Зафиксируем [$945$]. При этом рассмотрим функцию
При этом x может меняться от [$960$]/2-[$945$] до [$960$]/2 (не включая) и максимум достигается при x=90-[$945$]/2, а минимум на концах. При x = [$960$]/2-[$945$] функция равна 1+cos [$945$]. На правом конце [$946$] и [$947$] меняются местами. Так как левый и правый концы соответствуют прямоугольному треугольнику, значения функции больше 1+cos [$945$], а сумма углов 1+cos [$945$]+ sin [$945$]
Воспользуемся формулой
Отсюда
Суммируя по всем сторонам треугольника
Пытаемся доказать, что
, при условии, что Пусть [$945$] - наименьший угол. Зафиксируем [$945$]. При этом рассмотрим функцию
При этом x может меняться от [$960$]/2-[$945$] до [$960$]/2 (не включая) и максимум достигается при x=90-[$945$]/2, а минимум на концах. При x = [$960$]/2-[$945$] функция равна 1+cos [$945$]. На правом конце [$946$] и [$947$] меняются местами. Так как левый и правый концы соответствуют прямоугольному треугольнику, значения функции больше 1+cos [$945$], а сумма углов 1+cos [$945$]+ sin [$945$]
5
11.05.2011, 13:56
общий
Адресаты:
Асмик александровна! Такая формула разве есть:sin(a+b)=2sin((a+b)/2)cos((a+b)/2)?
Форма ответа
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