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