Odpowiedź:
Szczegółowe wyjaśnienie:
[tex]sin(\alpha) + cos(\alpha) = \frac{4}{5}\\\\(sin(\alpha) + cos(\alpha))^2 = \frac{16}{25}\\\\sin^2(\alpha) + 2*sin(\alpha)cos(\alpha) + cos^2(\alpha) = \frac{16}{25}\\\\sin^2(\alpha) + cos^2(\alpha) + 2*sin(\alpha)cos(\alpha) = \frac{16}{25}\\\\1 + 2*sin(\alpha)cos(\alpha) = \frac{16}{25}\\\\2*sin(\alpha)cos(\alpha) = \frac{16}{25} - 1\\ \\2*sin(\alpha)cos(\alpha) = - \frac{9}{25}\\\\sin(2\alpha) = - \frac{9}{25}\\[/tex]
