Question

Qual o valor de sen x, sabendo que cos x + 2. sen x=2 ?

Answer 1

$cos\ x+2\ sen\ x = 2\\\\ cos\ x = 2-2sen\ x\\\\\ sen^2x +cos^2x = 1\\\\\ sen^2x+(2-2sen\ x)^2=1\\\\ sen^2x+4-8sen\ x+4sen^2x = 1\\\\ 5sen^2x-8sen\ x = -3\\\\ sen\ x(5sen\ x-8)=-3$

$sen\ x(5sen\ x-8)=-3\\\\ sen\ x = -3\\\\\ 5sen\ x-8=-3\\\\ 5sen\ x = 5\\\\ sen\ x = 1$

$cos\ x = 2-2(-3)\\\\ cos\ x = 8\\\\ cos\ x = 2-2\\\\ cos\ x = 0$

$\boxed{\therefore\ sen\ x = -3,\ sen\ x = 1}$