Question

calcule o sen 2a , sabendo que sen a - cos a : 2/5

Answer 1

Vamos elevar ao quadrado ambos os lados:

$sen\ a-cos\ a=\frac{2}{5}\\\\ (sen\ a-cos\ a)^2=(\frac{2}{5})^2\\\\ sen^2a-2sen\ a\ cos\ a+cos^2a=\frac{4}{25}\\\\ \boxed{sen^2a+cos^2a=1}\\\\ \boxed{sen2\ a=2sen\ a\ cos\ a}\\\\ 1-sen2\ a=\frac{4}{25}$

$sen\ 2a = 1-\frac{4}{25}\\\\ sen\ 2a=\frac{25}{25}-\frac{4}{25}\\\\ \boxed{\boxed{sen\ 2a=\frac{21}{25}}}$