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Консультация № 145328
28.09.2008, 18:40
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1
Здраствуйте уважаемые сотрудники портала rusqag, я обращаюсь вам за помощью в решение данного примера (1-sin(a)/1-cosec(a))^4+cos^4(a)+2sin^2(a)cos^2(a)
Приложение:
^2-квадрат, ^4-четвертая степень
Заранее спасибо!
Приложение:
^2-квадрат, ^4-четвертая степень
Заранее спасибо!
Обсуждение
Неизвестный
29.09.2008, 22:29
общий
это ответ
Здравствуйте, Алексей Бобырев Васильевич!
В первой дроби числитель и знаменатель домножаем на синус получим (-sina)^4 .
(1-sin(a)/1-cosec(a))^4+cos^4(a)+2sin^2(a)cos^2(a) = ((sina*(1-sina)/(sina-1))^4) + ((cosa)^4) +
+ 2*((sina*cosa)^2) = ((sina)^4) + 2*((sina)^2)*((cosa)^4) + ((cosa)^4) = [((sina)^2)+((cosa)^2)]^2 =
= 1^2 = 1 .
В первой дроби числитель и знаменатель домножаем на синус получим (-sina)^4 .
(1-sin(a)/1-cosec(a))^4+cos^4(a)+2sin^2(a)cos^2(a) = ((sina*(1-sina)/(sina-1))^4) + ((cosa)^4) +
+ 2*((sina*cosa)^2) = ((sina)^4) + 2*((sina)^2)*((cosa)^4) + ((cosa)^4) = [((sina)^2)+((cosa)^2)]^2 =
= 1^2 = 1 .
Форма ответа
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