Question

Помогите, Тригонометрия

Answer 1

Ответ:

$\sin( \alpha - \beta ) = \sin( \alpha ) \times \cos( \beta ) - \sin( \beta ) \times \cos( \alpha ) \\ \cos( \alpha + \beta ) = \cos( \alpha ) \times \cos( \beta ) - \sin( \alpha ) \times \sin( \beta )$

$\cos( \alpha ) = \sqrt{1 - { \sin( \alpha ) }^{2} } = \sqrt{1 - \frac{64}{289} } = \sqrt{ \frac{225}{289} } = \frac{5}{17}$

$\sin( \beta ) = \sqrt{1 - { \cos( \beta ) }^{2} } = \sqrt{1 - \frac{16}{25} } = \sqrt{ \frac{9}{25} } = \frac{3}{5}$

$\sin( \alpha - \beta ) = \frac{8}{17} \times \frac{4}{5} - \frac{3}{5} \times \frac{5}{17} = \frac{32 - 15}{17 \times 5} = \frac{17}{105}$

$\cos( \alpha + \beta ) = \frac{5}{17} \times \frac{4}{5} - \frac{3}{5} \times \frac{8}{17} = \frac{20 - 18}{105} = \frac{2}{105}$