Question

Если tg $\frac{\alpha}{2}$ = -2, найдите значение выражения sin α + 2cos α

Answer 1

$sin(\alpha) = \frac{2tg(\frac{\alpha}{2})}{1 + tg^{2}(\frac{\alpha}{2})} \\ cos(\alpha) = \frac{1 - tg^{2}(\frac{\alpha}{2})}{1 + tg^{2}(\frac{\alpha}{2})} \\ sin(\alpha) + 2cos(\alpha) = \frac{-4}{5} + \frac{2 * (-3)}{5} = -2$