Question

Помогите пожалуйста срочно

Answer 1

Ответ: sin(α-β)=84/85.

Объяснение:

$\displaystyle\\1)\ cos\alpha =\frac{3}{5}\ \ \ \ \frac{3\pi }{2} < \alpha < 2\pi \\\\sin^2\alpha +cos^2\alpha =1\\\\sin^2\alpha =1-cos^2\alpha=1-(\frac{3}{5})^2=1-\frac{9}{25}=\frac{25*1-9}{25}=\frac{16}{25} \\\\\sin\alpha =б\sqrt{\frac{16}{25} } =б\frac{4}{5}\\\\ \frac{3\pi }{2} < \alpha < 2\pi \ \ \ \ \Rightarrow\\\\sin\alpha=-\frac{4}{5} .$

$\displaystyle\\2)\ sin\beta =-\frac{8}{17 }\ \ \ \ \pi < \beta < \frac{3\pi }{2} \\\\sin^2\beta +cos^2\beta =1\\\\cos^2\beta =1-sin^2\beta =1-(-\frac{8}{17} )^2=1-\frac{64}{289} =\frac{289*1-64}{289} =\frac{225}{289}.\\\\ cos\beta =б\sqrt{\frac{225}{289} } =б\frac{15}{17}.\\\\\pi < \beta < \frac{3\pi }{2} \ \ \ \ \Rightarrow\\\\cos\beta =-\frac{15}{17} .$

$\displaystyle\\3)\ sin(\alpha -\beta )=sin\alpha *cos\beta -sin\beta *cos\alpha =(-\frac{4}{5})*(-\frac{15}{17})-(-\frac{8}{17})*\frac{3}{5} =\\\\ =\frac{60}{85}+\frac{24}{85} =\frac{60+24}{85}=\frac{84}{85} =\frac{60}{85}+\frac{24}{85} =\frac{60+24}{85}=\frac{84}{85}.$