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 = (\pi)/(2) \: x = (3\pi)/(2)`
and when

`1 + 2 \sin(x) = 0`
so

`2 \sin(x ) = - 1`

`\sin(x) = ( - 1)/(2)`
so

`x = (3\pi)/(2) - (\pi)/(3)`
and

`x = (3\pi)/(2) + (\pi)/(3)`