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