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