10
sin
2
x
+
2
3
sin
x
cos
x
+
4
cos
2
x
=
7
10
sin
2
x
+
2
3
sin
x
cos
x
+
4
cos
2
x
−
7
cos
2
x
−
7
sin
2
x
=
0
3
sin
2
x
+
2
3
sin
x
cos
x
−
3
cos
2
x
=
0
3
tan
2
x
+
2
3
tan
x
−
3
=
0
tan
x
12
=
3
±
(
3
)
2
+
9
3
=
3
±
12
3
=
3
±
2
3
3
→
→
{
tan
x
1
=
3
+
2
3
3
=
3
→
x
1
=
π
3
+
k
π
tan
x
2
=
3
−
2
3
3
=
−
3
3
→
x
2
=
−
π
6
+
k
π
10 sin^2 x + 2 sqrt 3 sin x cos x + 4 cos^2 x = 7 newline newline
10 sin^2 x + 2 sqrt 3 sin x cos x + 4 cos^2 x - 7 cos^2 x - 7 sin^2 x = 0 newline newline
3 sin^2 x + 2 sqrt 3 sin x cos x -3 cos^2 x = 0 newline newline
3 tan^2 x + 2 sqrt 3 tan x -3 = 0 newline newline
tan x_12= { sqrt 3 +- sqrt{(sqrt 3 )^2+9} } over {3} = { sqrt 3 +- sqrt{12} } over {3}={ sqrt 3 +- 2 sqrt{3} } over {3} toward "" newline newline
toward left lbrace stack{tan x_1 = { sqrt 3 + 2 sqrt{3} } over {3} = sqrt 3 toward x_1 ={ %pi over 3} + k %pi # tan x_2 ={ sqrt 3 - 2 sqrt{3} } over {3} =- {sqrt 3 over 3} toward x_2= -{ %pi over 6} + k %pi } right none