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

Question

cos x + 2 cos x sin x = 0

would the answer be 7pi/6 , 11pi/6 ?

Answer 1

factor it
cosx(1 + 2sinx) = 0
cosx = 0 or sinx = -1/2

if cosx = 0
x = π/2 , 3π/2

for sinx = -1/2, we know x is in III or IV
we also know that sin π/6 = + 1/2
x = π + π/6 or 7π/6
x = 2π - π/6 = 11π/6

so you had 2 of the 4 answers