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Консультация № 159940
08.02.2009, 16:19
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Здравствуйте! Помогите пожалуйста!
4sin8A, если ctg4A=-3
Заранее благодарю.
4sin8A, если ctg4A=-3
Заранее благодарю.
Обсуждение
Неизвестный
08.02.2009, 23:43
общий
это ответ
Здравствуйте, отарова лизавета !
ctg4A=cos4A/sin4A=-3 => cos4A=-3sin4A
(cos4A)^2+(sin4A)^2=1 => 10*(sin4A)^2=1 (подставили полученное выше равенство) => (sin4A)^2=1/10, (cos4a)^2=9/10 => sin4A=1/sqrt(10), cos4A=-3/sqrt(10) (sqrt - квадратный корень)
Возможно, что sin4A=-1/sqrt(10), cos4A=3/sqrt(10), но на ответ это не влияет. В любом случае, 4*sin8A=8*sin4A*cos4A = -8*(1/sqrt(10))*(3/sqrt(10))=-24/10
ctg4A=cos4A/sin4A=-3 => cos4A=-3sin4A
(cos4A)^2+(sin4A)^2=1 => 10*(sin4A)^2=1 (подставили полученное выше равенство) => (sin4A)^2=1/10, (cos4a)^2=9/10 => sin4A=1/sqrt(10), cos4A=-3/sqrt(10) (sqrt - квадратный корень)
Возможно, что sin4A=-1/sqrt(10), cos4A=3/sqrt(10), но на ответ это не влияет. В любом случае, 4*sin8A=8*sin4A*cos4A = -8*(1/sqrt(10))*(3/sqrt(10))=-24/10
Форма ответа
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