Question

Solve the equation on the interval [0, 2π). cos x + 2 cos x sin x = 0

Answer 1

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