Question

 Помогите пожалуиста срочно нужно))))))))))Заранее спасибо))))))))))   Докажите тождество: sin2a-2sina / cosa-1= 2sina

Answer 1

Окей, я попробую ответить на ваш вопрос на русском языке.

Для начала, мы должны доказать тождество: sin^2(a) - 2sin(a)/cos(a) - 1 = 2sin(a).

Давайте начнем с левой стороны:

sin^2(a) - 2sin(a)/cos(a) - 1

Мы можем представить sin(a) / cos(a) как tan(a), используя тригонометрическое тождество sin(a) / cos(a) = tan(a).

Теперь наше тождество выглядит так:

sin^2(a) - 2tan(a) - 1

Мы также можем заменить sin^2(a) на 1 - cos^2(a), используя тригонометрическое тождество sin^2(a) + cos^2(a) = 1.

Теперь наше тождество выглядит так:

1 - cos^2(a) - 2tan(a) - 1

Мы можем упростить это выражение, объединив первый и третий члены:

- cos^2(a) - 2tan(a)

Мы также можем заменить tan(a) на sin(a) / cos(a) и упростить дальше:

- cos^2(a) - 2sin(a) / cos(a)

Мы можем представить cos^2(a) как 1 - sin^2(a), используя тригонометрическое тождество sin^2(a) + cos^2(a) = 1.

Теперь наше тождество выглядит так:

1 - sin^2(a) - 2sin(a) / cos(a)

Мы также знаем, что 1 можно представить как cos^2(a) + sin^2(a), используя тождество sin^2(a) + cos^2(a) = 1.

Теперь наше тождество выглядит так:

cos^2(a) + sin^2(a) - sin^2(a) - 2sin(a) / cos(a)

Мы можем упростить это выражение, объединив первый и третий члены:

cos^2(a) - 2sin(a) / cos(a)

Мы знаем, что cos(a) / cos(a) равно 1, поэтому мы можем упростить дальше:

cos^2(a) - 2sin(a) / cos(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a)

cos^2(a) - 2sin(a) * cos(a) / cos(a