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Автор - galyalll

Помогите с седьмым задание пожалуйста! Тригонометрия

Ответ

Проверено экспертом

Автор - Universalka

(Cosα - Sinα)² + 3SinαCosα = Cos²α - 2SinαCosα + Sin²α + 3SinαCosα =

= 1 + SinαCosα

По условию :

Cosα + Sinα = 0,9

Возведём обе части в квадрат :

(Cosα + Sinα)² = 0,9²

Cos²α + 2SinαCosα + Sin²α = 0,81

1 + 2SinαCosα = 0,81

2SinαCosα = 0,81 - 1

2SinαCosα = - 0,19

SinαCosα = - 0,095

Следовательно :

(Cosα - Sinα)² + 3SinαCosα = 1 + SinαCosα = 1 - 0,095 = 0,905

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