Предмет: Алгебра, автор: barbar1k1337

Помогите доказать тождество

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Ответы

Автор ответа: liftec74

Ответ:

Объяснение:

Преобразуем числитель

1-сos2α+sin2α =1-(cos²α-sin²α)+2sinαcosα=

1-cos²a +sin²α+2sinαcosα =sin²α+sin²α+2sinα·cosα=2sin²α+2sinα·cosα=

=2sinα(sinα+cosα)

Преобразуем знаменатель

1+сos2α+sin2α =1+(cos²α-sin²α)+2sinαcosα=

1+cos²a -sin²α+2sinαcosα =cos²α+cos²α+2sinα·cosα=2cos²α+2sinα·cosα= 2cosα(cosα+sinα)

Тогда все дробное выражение равно

2sinα(sinα+cosα) / 2cosα(cosα+sinα) =sinα/cosα=tgα

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