Вычислите sin2a, если tga=1/2

Решите задачу:

$\displaystyle tga= \frac{1}{2}; a\in I; IV\\\\sin2a= 2sina*cosa\\\\1+tg^2a= \frac{1}{cos^2a}\\\\1+ \frac{1}{4}= \frac{1}{cos^2a}\\\\ \frac{5}{4}= \frac{1}{cos^2a}\\\\cos^2a= \frac{4}{5}$

$\displaystyle sin^2a=1- \frac{4}{5}= \frac{1}{5}$

$\displaystyle cosa= \pm\frac{2}{ \sqrt{5}}; sina=\pm \frac{1}{ \sqrt{5}}\\\\sin2a=2* \frac{2}{ \sqrt{5}}* \frac{1}{ \sqrt{5}}= \frac{4}{5}$