Автор - noname09011

Здравствуйте. Скажите, пожалуйста, как получилось такое преобразование? Тригонометрия

Ответ

Автор - Indentuum

frac{2sin^2(frac{pi}{4} - alpha)}{2cos^2(frac{pi}{4} - alpha)} = frac{2frac{1 - cos(frac{pi}{2} - 2alpha)}{2}}{2frac{1 + cos(frac{pi}{2} - 2alpha)}{2}} = frac{1 - cos(frac{pi}{2} - 2alpha)}{1 + cos(frac{pi}{2} - 2alpha)} = frac{1 - sin(2alpha)}{1 + sin(2alpha)} = frac{1 - 2sin(alpha)cos(alpha)}{1 + 2sin(alpha)cos(alpha)} = \\= frac{sin^2(alpha) + cos^2(alpha) - 2sin(alpha)cos(alpha)}{sin^2(alpha) + cos^2(alpha) + 2sin(alpha)cos(alpha)} =

= frac{(cos(alpha) - sin(alpha))^2}{(cos(alpha) + sin(alpha))^2}

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