take a common factor of cos(x)
[tex] \cos(x) (1 + 2 \sin(x) ) = 0[/tex]
then by zero multplication rules
[tex] \cos(x) = 0[/tex]
[tex]x = \frac{\pi}{2} \: x = \frac{3\pi}{2} [/tex]
and when
[tex]1 + 2 \sin(x) = 0[/tex]
so
[tex]2 \sin(x ) = - 1[/tex]
[tex] \sin(x) = \frac{ - 1}{2} [/tex]
so
[tex]x = \frac{3\pi}{2} - \frac{\pi}{3} [/tex]
and
[tex]x = \frac{3\pi}{2} + \frac{\pi}{3} [/tex]
