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Консультация № 176316
26.01.2010, 16:13
42.70 руб.
0
3
1
Уважаемые эксперты, помогите пожалуйста решить уравнение:
sin 3x/ |cos x| = sin 6x/ sin 4x
sin 3x/ |cos x| = sin 6x/ sin 4x
Обсуждение
27.01.2010, 16:15
общий
STASSY:
Здравствуйте, STASSY!
В итоге задача сводится к решению двух кубичных уравнений. К чему бы это? Могу выложить свои выкладки к решению уравнения (sin 3x)/(cos x) = (sin 6x)/(sin 4x), которое получается из заданного уравнения при неотрицательных значениях cos x. Я остановился на уравнении 2(tg x)3 - 3(tg x)2 - 2tg x + 1 = 0, которое путем деления на 2 приводится к виду полного кубичного уравнения и решается громоздким путем при помощи формул Кардано. Но надо ли это?
А получилось такое уравнение из уравнения tg 3x + tg x = 2 после подстановки в него выражения tg 3x через tg x. В свою очередь, уравнение
tg 3x + tg x = 2 легко получается из исходного уравнения, если учитывать, что tg 3x + tg x = sin 4x - 2(cos 3x)cos x.
Более рационального решения задания я не смог найти. Но указанное решение считаю тупиковым и поэтому не выложил в виде ответа.
С уважением.
Здравствуйте, STASSY!
В итоге задача сводится к решению двух кубичных уравнений. К чему бы это? Могу выложить свои выкладки к решению уравнения (sin 3x)/(cos x) = (sin 6x)/(sin 4x), которое получается из заданного уравнения при неотрицательных значениях cos x. Я остановился на уравнении 2(tg x)3 - 3(tg x)2 - 2tg x + 1 = 0, которое путем деления на 2 приводится к виду полного кубичного уравнения и решается громоздким путем при помощи формул Кардано. Но надо ли это?
А получилось такое уравнение из уравнения tg 3x + tg x = 2 после подстановки в него выражения tg 3x через tg x. В свою очередь, уравнение
tg 3x + tg x = 2 легко получается из исходного уравнения, если учитывать, что tg 3x + tg x = sin 4x - 2(cos 3x)cos x.
Более рационального решения задания я не смог найти. Но указанное решение считаю тупиковым и поэтому не выложил в виде ответа.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
27.01.2010, 16:17
общий
STASSY:
По ходу решения получалось уравнение sin 4x - cos 4x - cos 2x = 0. Но его я решить не сумел...
По ходу решения получалось уравнение sin 4x - cos 4x - cos 2x = 0. Но его я решить не сумел...
Об авторе:
Facta loquuntur.
Facta loquuntur.
29.01.2010, 11:01
общий
это ответ
Здравствуйте, STASSY.
По этой ссылке Вы можете увидеть предложенное мной решение Вашей задачи. Оно небесспорно, но учитывая, что никто из экспертов не ответил на заданный Вами вопрос, я решил изложить его.
Рад был помочь!
С уважением.
По этой ссылке Вы можете увидеть предложенное мной решение Вашей задачи. Оно небесспорно, но учитывая, что никто из экспертов не ответил на заданный Вами вопрос, я решил изложить его.
Рад был помочь!
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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