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Консультация № 172491
22.09.2009, 18:03
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Здравствуйте уважаемые эксперты. прошу вас помоч решить уравнение 3+sin2х=4(1-соs квадрат х). Заранее спасибо
Обсуждение
22.09.2009, 19:06
общий
это ответ
Здравствуйте, Попов Сергей Владимирович.3+2sinxcosx-4sin^2 x=0.Делим обе части на сos^2 x. cosxне равен 0 так как в противном случае sinx=1. 3/cos^2 x+2tgx -4tg^2 x=0 3+3tg^2 x+2tgx -4tg^2 x=0 tg^2 x-2tgx +3=0 tgx=-1 и tgx=3 x=-п/4+пк и х=arctg3+пк к-целое число
Неизвестный
22.09.2009, 19:12
общий
это ответ
Здравствуйте, Попов Сергей Владимирович.
3+sin2х=4(1-соs2х)
3+sin2х=4sin2x
1+sin2x + 2*(1-2sin2x)=0
1+sin2x+2cos2x=0
([$8730$]5) * (sin2x * cos(arccos(1/[$8730$]5)) + cos2x * sin(arcsin(2/[$8730$]5))) = -1
sin(2x+arcsin(2/[$8730$]5))=-1/([$8730$]5)
2x+arcsin(2/[$8730$]5)=(-1)n+1*arcsin(1/[$8730$]5)+пn, где n[$8712$]Z
x = (1/2)*((-1)n+1*arcsin(1/[$8730$]5) - arcsin(2/[$8730$]5)) + пn/2, где n[$8712$]Z
В принципе, это ответ.
3+sin2х=4(1-соs2х)
3+sin2х=4sin2x
1+sin2x + 2*(1-2sin2x)=0
1+sin2x+2cos2x=0
([$8730$]5) * (sin2x * cos(arccos(1/[$8730$]5)) + cos2x * sin(arcsin(2/[$8730$]5))) = -1
sin(2x+arcsin(2/[$8730$]5))=-1/([$8730$]5)
2x+arcsin(2/[$8730$]5)=(-1)n+1*arcsin(1/[$8730$]5)+пn, где n[$8712$]Z
x = (1/2)*((-1)n+1*arcsin(1/[$8730$]5) - arcsin(2/[$8730$]5)) + пn/2, где n[$8712$]Z
В принципе, это ответ.
Форма ответа
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