Question

Solve the equation on the interval [0, 2π).

cos x + 2 cos x sin x = 0
A. pi/2, 7pi/6, 3pi/2

B. pi/2, 7pi/6, 3pi/2, 11pi/6

C. 7pi/6, 11pi/6 2π

Answer 1

$\cos x+2\cos x\sin x=\cos x(1+2\sin x)=0$

$\cos x=0$ in the given interval when $x=\dfrac\pi2,\dfrac{3\pi}2$.

$1+2\sin x=0\implies \sin x=-\dfrac12$ when $x=\dfrac{7\pi}6,\dfrac{11\pi}6$.

Answer 2

Answer: -(sqrt 3/2)

Step-by-step explanation: