Question

Вычислить cos(2arccos5/12)

Answer 1

cos(arccos5/12)^2 - sin(arccos5/12)^2=
$( \frac{5}{12} ) {}^{2} - ({1 - ( \frac{5}{12}) {}^{2} } ) = \\ (\frac{5}{12} ) {}^{2} - 1 + (\frac{5}{12} ) {}^{2} = \\ 2 \times ( \frac{5}{12} ) {}^{2} - 1 = 2 \times \frac{25}{144} - 1 = \\ \frac{25}{72} - \frac{72}{72} = - \frac{47}{72}$
ответ: - 47/72