Question

Вычислите sin(a-B), если sina = 4/5, cosB = -5/13, П/2<а<П, П/2<В<П

Answer 1

Sin(a-b)=sinacosb-cosasinb
sinb=$\sqrt{1-cos^2b}= \sqrt{1- \frac{25}{169} } = \frac{12}{13}$
cosa=$- \sqrt{1-sin^2a}= -\sqrt{1- \frac{16}{25} } = -\frac{3}{5}$
sin(a-b)=$\frac{4}{5} *(- \frac{5}{13} )-(- \frac{3}{5} )* \frac{12}{13} =- \frac{4}{13} + \frac{36}{65} = \frac{16}{65}$