Question

Даю 25 баллов!
Найдите sin2a и cos2a если cosa (на фото)

Answer 1

Ответ:

$\sin( \alpha ) = \sqrt{1 - \cos {}^{2} ( \alpha ) } \\ \sin( \alpha ) = - \sqrt{1 - \frac{64}{289} } = - \sqrt{ \frac{225}{289} } = - \frac{15}{17} \\ \\ \sin( 2 \alpha ) = 2 \sin( \alpha ) \cos( \alpha ) = \\ = 2 \times ( - \frac{15}{17} ) \times \frac{8}{17} = - \frac{240}{289} \\ \\ \cos( 2\alpha ) = \cos {}^{2} ( \alpha ) - \sin {}^{2} ( \alpha ) = \\ = \frac{64}{289} - \frac{225}{289} = - \frac{161}{289}$