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Консультация № 157234
10.01.2009, 17:50
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Помогите решить пожайлуста тотожность.
(cosα-〖cosβ)〗^2+〖(sinα-sinβ)〗^2=4〖sin〗^2 (α-β)/2
(cosα-〖cosβ)〗^2+〖(sinα-sinβ)〗^2=4〖sin〗^2 (α-β)/2
Обсуждение
Неизвестный
10.01.2009, 20:07
общий
это ответ
Здравствуйте, Glazko Maxim Olegovi4!
(cos а - cos b)^2 + (sin a - sin b)^2 = cos^2 a - 2*cos a*cos b + cos^2 b + sin^2 a - 2*sin a*sin b + sin^2 b = 2 - 2*cos a*cos b - 2* sin a*sin b = 2 - cos(a-b) - cos(a+b) - cos(a-b) + cos(a+b) = 2 - 2*cos(a-b) = 2*(1-cos(a-b)) = 2*2*sin^2 (a-b)/2 = 4*sin^2 (a-b)/2
(cos а - cos b)^2 + (sin a - sin b)^2 = cos^2 a - 2*cos a*cos b + cos^2 b + sin^2 a - 2*sin a*sin b + sin^2 b = 2 - 2*cos a*cos b - 2* sin a*sin b = 2 - cos(a-b) - cos(a+b) - cos(a-b) + cos(a+b) = 2 - 2*cos(a-b) = 2*(1-cos(a-b)) = 2*2*sin^2 (a-b)/2 = 4*sin^2 (a-b)/2
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