Question

Solve the equation on the interval [ 0, 2 pi] (tan x + ?3)(2cos x + 1) = 0

Answer 1

you have a typo in your first bracket, what is (tanx + ?3) supposed to be ?

set each of the brackets equal to zero, I will do the second one

2cosx +1 = 0
cosx = -1/2
so x must be in the second or third quadrant according to the CAST rule.

(the cos 60º=+1/2)

so x = 180-60 = 120º or 2pi/3 radians
or x = 180 + 60 = 240º or 4pi/3 radians

do the same thing with the first bracket after you fix the typo.

Answer 2

(tan x + sqrt 3)(2 cos x + 1)=0

Answer 3

so from the first bracket,
tan x = - √3

now isn't tan 60 = +√3 ?

can you take it from there following the method I used for the second bracket?

let me know what you got.

Answer 4

Thanks I'll let you know what I get