Question

Вычислите sin(2a) при tg(a)=-7

Answer 1

$tga=-7 \\\\ 1+tg^2a= \frac{1}{cos^2a} \\\\ 1+49=\frac{1}{cos^2a} \\\\ cos^2a= \frac{1}{50} \\\\ cosa= \frac{1 }{5 \sqrt{2} } \\\\ sina=- \sqrt{1- \frac{1}{50} } =- \frac{7}{5 \sqrt{2} } \\\\ sin2a=2sinacosa=2*(- \frac{7}{5 \sqrt{2} } )* \frac{1}{5 \sqrt{2} } =- \frac{7}{25}$