sin
2
x
+
4
3
sin
x
cos
x
+
cos
2
x
+
2
=
0
sin
2
x
+
4
3
sin
x
cos
x
+
cos
2
x
+
2
cos
2
x
+
2
sin
2
x
=
0
3
sin
2
x
+
4
3
sin
x
cos
x
+
3
cos
2
x
=
0
3
tan
2
x
+
4
3
tan
x
+
3
=
0
tan
x
12
=
−
4
3
±
(
4
3
)
2
−
36
6
=
−
4
3
±
48
−
36
6
=
−
4
3
±
12
6
=
−
4
3
±
2
3
6
→
→
{
tan
x
1
=
−
4
3
+
2
3
6
=
−
3
3
→
x
1
=
−
π
6
+
k
π
tan
x
2
=
−
4
3
−
2
3
6
=
−
3
→
x
2
=
2
π
3
+
k
π
sin^2 x + 4 sqrt 3 sin x cos x +cos^2 x + 2 = 0 newline newline
sin^2 x + 4 sqrt 3 sin x cos x +cos^2 x + 2 cos^2 x + 2 sin^2 x = 0 newline newline
3 sin^2 x + 4 sqrt 3 sin x cos x +3 cos^2 x = 0 newline newline
3 tan^2 x + 4 sqrt 3 tan x +3 = 0 newline newline
tan x_12= { -4 sqrt 3 +- sqrt{(4 sqrt 3 )^2-36} } over { 6 } ={ -4 sqrt 3 +- sqrt{48-36} } over { 6} = { -4 sqrt 3 +- sqrt{12} } over { 6 }= { - 4 sqrt 3 +- 2 sqrt{3} } over { 6 } toward "" newline newline
toward left lbrace stack{tan x_1 = { - 4 sqrt 3 + 2 sqrt{3} } over { 6 } = - {sqrt 3 over 3} toward x_1 =-{ %pi over 6} + k %pi # tan x_2 = { - 4 sqrt 3 - 2 sqrt{3} } over { 6 }=- sqrt 3 toward x_2= {2 %pi} over 3 + k %pi} right none