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Консультация № 145347
28.09.2008, 19:49
0.00 руб.
28.09.2008, 20:36
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Доброе здоровьице уважаемые експерты!Прошу помочь мне в решении нескольких задач!Сам я дурак и не могу их решить!Заранее решившему поклон!
8)преобразовать в произведение sin2(альфа) + sin2(бета) + 2sin(альфа)sin(бета)cos(альфа+бета)
8)преобразовать в произведение sin2(альфа) + sin2(бета) + 2sin(альфа)sin(бета)cos(альфа+бета)
Обсуждение
Неизвестный
29.09.2008, 00:50
общий
это ответ
Здравствуйте, Бортников Артём Михайлович!
Путём долгих выводов я пришёл к (sin(a+b))^2 , наверное , возмжны варианты .
sin2(альфа) + sin2(бета) + 2sin(альфа)sin(бета)cos(альфа+бета) = ((sina)^2)+((sinb)^2)-2*((sina)^2)*
*((sinb)^2)+2*(sina)*(cosa)*(sinb)*(cosb) = ((sina)^2)*(1-2*((sinb)^2))+((sinb)^2)+(1/2)*(sin(2*a))*
*(sin(2*b)) = ((sina)^2)*(cos(2*b))+(1/2)-(1/2)*(cos(2*b))+(1/2)*(sin(2*a))*(sin(2*b)) = (1/2)-(1/2)*
*(cos(2*b))*(1-2*((sina)^2)+(1/2)*(sin(2*a))*(sin(2*b)) = (1/2)-(1/2)*((cos(2*a))*(cos(2*b))-(sin(2*a))*
*(sin(2*b))) = (1/2)*(1-cos(2*a+2*b)) = (1/2)*(1-1+2*((sin(a+b))^2)) = (1/2)*2*((sin(a+b))^2) =
= ((sin(a+b))^2) .
OTBET : sin2(альфа) + sin2(бета) + 2sin(альфа)sin(бета)cos(альфа+бета) = ((sin(a+b))^2) .
Путём долгих выводов я пришёл к (sin(a+b))^2 , наверное , возмжны варианты .
sin2(альфа) + sin2(бета) + 2sin(альфа)sin(бета)cos(альфа+бета) = ((sina)^2)+((sinb)^2)-2*((sina)^2)*
*((sinb)^2)+2*(sina)*(cosa)*(sinb)*(cosb) = ((sina)^2)*(1-2*((sinb)^2))+((sinb)^2)+(1/2)*(sin(2*a))*
*(sin(2*b)) = ((sina)^2)*(cos(2*b))+(1/2)-(1/2)*(cos(2*b))+(1/2)*(sin(2*a))*(sin(2*b)) = (1/2)-(1/2)*
*(cos(2*b))*(1-2*((sina)^2)+(1/2)*(sin(2*a))*(sin(2*b)) = (1/2)-(1/2)*((cos(2*a))*(cos(2*b))-(sin(2*a))*
*(sin(2*b))) = (1/2)*(1-cos(2*a+2*b)) = (1/2)*(1-1+2*((sin(a+b))^2)) = (1/2)*2*((sin(a+b))^2) =
= ((sin(a+b))^2) .
OTBET : sin2(альфа) + sin2(бета) + 2sin(альфа)sin(бета)cos(альфа+бета) = ((sin(a+b))^2) .
Форма ответа
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