sin
π
60
=
cos
29
π
60
=
sin
3
∘
=
cos
87
∘
=
2
(
3
+
1
)
(
5
−
1
)
−
2
(
3
−
1
)
5
+
5
16
,
{\displaystyle \sin {\frac {\pi }{60}}=\cos {\frac {29\,\pi }{60}}=\sin 3^{\circ }=\cos 87^{\circ }={\frac {{\sqrt {2}}({\sqrt {3}}+1)({\sqrt {5}}-1)-2({\sqrt {3}}-1){\sqrt {5+{\sqrt {5}}}}}{16}},}
cos
π
60
=
sin
29
π
60
=
cos
3
∘
=
sin
87
∘
=
2
(
3
−
1
)
(
5
−
1
)
+
2
(
3
+
1
)
5
+
5
16
,
{\displaystyle \cos {\frac {\pi }{60}}=\sin {\frac {29\,\pi }{60}}=\cos 3^{\circ }=\sin 87^{\circ }={\frac {{\sqrt {2}}({\sqrt {3}}-1)({\sqrt {5}}-1)+2({\sqrt {3}}+1){\sqrt {5+{\sqrt {5}}}}}{16}},}
tg
π
60
=
ctg
29
π
60
=
tg
3
∘
=
ctg
87
∘
=
2
(
5
+
2
)
−
3
(
5
+
3
)
+
(
2
−
3
)
(
3
(
5
+
1
)
−
2
)
5
−
2
5
2
,
{\displaystyle \operatorname {tg} {\frac {\pi }{60}}=\operatorname {ctg} {\frac {29\,\pi }{60}}=\operatorname {tg} 3^{\circ }=\operatorname {ctg} 87^{\circ }={\frac {2({\sqrt {5}}+2)-{\sqrt {3}}({\sqrt {5}}+3)+(2-{\sqrt {3}})({\sqrt {3}}({\sqrt {5}}+1)-2){\sqrt {5-2{\sqrt {5}}}}}{2}},}
ctg
π
60
=
tg
29
π
60
=
ctg
3
∘
=
tg
87
∘
=
2
(
2
(
5
+
2
)
+
3
(
5
+
3
)
)
+
(
3
(
5
−
1
)
+
2
)
2
(
25
+
11
5
)
4
,
{\displaystyle \operatorname {ctg} {\frac {\pi }{60}}=\operatorname {tg} {\frac {29\,\pi }{60}}=\operatorname {ctg} 3^{\circ }=\operatorname {tg} 87^{\circ }={\frac {2(2({\sqrt {5}}+2)+{\sqrt {3}}({\sqrt {5}}+3))+({\sqrt {3}}({\sqrt {5}}-1)+2){\sqrt {2(25+11{\sqrt {5}})}}}{4}},}
sin
π
30
=
cos
7
π
15
=
sin
6
∘
=
cos
84
∘
=
6
(
5
−
5
)
−
5
−
1
8
,
{\displaystyle \sin {\frac {\pi }{30}}=\cos {\frac {7\,\pi }{15}}=\sin 6^{\circ }=\cos 84^{\circ }={\frac {{\sqrt {6(5-{\sqrt {5}})}}-{\sqrt {5}}-1}{8}},}
cos
π
30
=
sin
7
π
15
=
cos
6
∘
=
sin
84
∘
=
2
(
5
−
5
)
+
3
(
5
+
1
)
8
,
{\displaystyle \cos {\frac {\pi }{30}}=\sin {\frac {7\,\pi }{15}}=\cos 6^{\circ }=\sin 84^{\circ }={\frac {{\sqrt {2(5-{\sqrt {5}})}}+{\sqrt {3}}({\sqrt {5}}+1)}{8}},}
tg
π
30
=
ctg
7
π
15
=
tg
6
∘
=
ctg
84
∘
=
2
(
5
−
5
)
−
3
(
5
−
1
)
2
,
{\displaystyle \operatorname {tg} {\frac {\pi }{30}}=\operatorname {ctg} {\frac {7\,\pi }{15}}=\operatorname {tg} 6^{\circ }=\operatorname {ctg} 84^{\circ }={\frac {{\sqrt {2(5-{\sqrt {5}})}}-{\sqrt {3}}({\sqrt {5}}-1)}{2}},}
ctg
π
30
=
tg
7
π
15
=
ctg
6
∘
=
tg
84
∘
=
2
(
25
+
11
5
)
+
3
(
5
+
3
)
2
,
{\displaystyle \operatorname {ctg} {\frac {\pi }{30}}=\operatorname {tg} {\frac {7\,\pi }{15}}=\operatorname {ctg} 6^{\circ }=\operatorname {tg} 84^{\circ }={\frac {{\sqrt {2(25+11{\sqrt {5}})}}+{\sqrt {3}}({\sqrt {5}}+3)}{2}},}
sin
π
20
=
cos
9
π
20
=
sin
9
∘
=
cos
81
∘
=
2
(
5
+
1
)
−
2
5
−
5
8
,
{\displaystyle \sin {\frac {\pi }{20}}=\cos {\frac {9\,\pi }{20}}=\sin 9^{\circ }=\cos 81^{\circ }={\frac {{\sqrt {2}}({\sqrt {5}}+1)-2{\sqrt {5-{\sqrt {5}}}}}{8}},}
cos
π
20
=
sin
9
π
20
=
cos
9
∘
=
sin
81
∘
=
2
(
5
+
1
)
+
2
5
−
5
8
,
{\displaystyle \cos {\frac {\pi }{20}}=\sin {\frac {9\,\pi }{20}}=\cos 9^{\circ }=\sin 81^{\circ }={\frac {{\sqrt {2}}({\sqrt {5}}+1)+2{\sqrt {5-{\sqrt {5}}}}}{8}},}
tg
π
20
=
ctg
9
π
20
=
tg
9
∘
=
ctg
81
∘
=
5
+
1
−
5
+
2
5
,
{\displaystyle \operatorname {tg} {\frac {\pi }{20}}=\operatorname {ctg} {\frac {9\,\pi }{20}}=\operatorname {tg} 9^{\circ }=\operatorname {ctg} 81^{\circ }={{\sqrt {5}}+1-{\sqrt {5+2{\sqrt {5}}}}},}
ctg
π
20
=
tg
9
π
20
=
ctg
9
∘
=
tg
81
∘
=
5
+
1
+
5
+
2
5
,
{\displaystyle \operatorname {ctg} {\frac {\pi }{20}}=\operatorname {tg} {\frac {9\,\pi }{20}}=\operatorname {ctg} 9^{\circ }=\operatorname {tg} 81^{\circ }={{\sqrt {5}}+1+{\sqrt {5+2{\sqrt {5}}}}},}
sin
π
15
=
cos
13
π
30
=
sin
12
∘
=
cos
78
∘
=
2
(
5
+
5
)
−
3
(
5
−
1
)
8
,
{\displaystyle \sin {\frac {\pi }{15}}=\cos {\frac {13\,\pi }{30}}=\sin 12^{\circ }=\cos 78^{\circ }={\frac {{\sqrt {2(5+{\sqrt {5}})}}-{\sqrt {3}}({\sqrt {5}}-1)}{8}},}
cos
π
15
=
sin
13
π
30
=
cos
12
∘
=
sin
78
∘
=
6
(
5
+
5
)
+
5
−
1
8
,
{\displaystyle \cos {\frac {\pi }{15}}=\sin {\frac {13\,\pi }{30}}=\cos 12^{\circ }=\sin 78^{\circ }={\frac {{\sqrt {6(5+{\sqrt {5}})}}+{\sqrt {5}}-1}{8}},}
tg
π
15
=
ctg
13
π
30
=
tg
12
∘
=
ctg
78
∘
=
3
(
3
−
5
)
−
2
(
25
−
11
5
)
2
,
{\displaystyle \operatorname {tg} {\frac {\pi }{15}}=\operatorname {ctg} {\frac {13\,\pi }{30}}=\operatorname {tg} 12^{\circ }=\operatorname {ctg} 78^{\circ }={\frac {{\sqrt {3}}(3-{\sqrt {5}})-{\sqrt {2(25-11{\sqrt {5}})}}}{2}},}
ctg
π
15
=
tg
13
π
30
=
ctg
12
∘
=
tg
78
∘
=
3
(
5
+
1
)
+
2
(
5
+
5
)
2
,
{\displaystyle \operatorname {ctg} {\frac {\pi }{15}}=\operatorname {tg} {\frac {13\,\pi }{30}}=\operatorname {ctg} 12^{\circ }=\operatorname {tg} 78^{\circ }={\frac {{\sqrt {3}}({\sqrt {5}}+1)+{\sqrt {2(5+{\sqrt {5}})}}}{2}},}
sin
7
π
60
=
cos
23
π
60
=
sin
21
∘
=
cos
69
∘
=
−
2
(
3
−
1
)
(
5
+
1
)
+
2
(
3
+
1
)
5
−
5
16
,
{\displaystyle \sin {\frac {7\,\pi }{60}}=\cos {\frac {23\,\pi }{60}}=\sin 21^{\circ }=\cos 69^{\circ }={\frac {-{\sqrt {2}}({\sqrt {3}}-1)({\sqrt {5}}+1)+2({\sqrt {3}}+1){\sqrt {5-{\sqrt {5}}}}}{16}},}
cos
7
π
60
=
sin
23
π
60
=
cos
21
∘
=
sin
69
∘
=
2
(
3
+
1
)
(
5
+
1
)
+
2
(
3
−
1
)
5
−
5
16
,
{\displaystyle \cos {\frac {7\,\pi }{60}}=\sin {\frac {23\,\pi }{60}}=\cos 21^{\circ }=\sin 69^{\circ }={\frac {{\sqrt {2}}({\sqrt {3}}+1)({\sqrt {5}}+1)+2({\sqrt {3}}-1){\sqrt {5-{\sqrt {5}}}}}{16}},}
tg
7
π
60
=
ctg
23
π
60
=
tg
21
∘
=
ctg
69
∘
=
2
(
2
(
5
−
2
)
−
3
(
3
−
5
)
)
+
(
3
(
5
+
1
)
−
2
)
2
(
25
−
11
5
)
4
,
{\displaystyle \operatorname {tg} {\frac {7\,\pi }{60}}=\operatorname {ctg} {\frac {23\,\pi }{60}}=\operatorname {tg} 21^{\circ }=\operatorname {ctg} 69^{\circ }={\frac {2(2({\sqrt {5}}-2)-{\sqrt {3}}(3-{\sqrt {5}}))+({\sqrt {3}}({\sqrt {5}}+1)-2){\sqrt {2(25-11{\sqrt {5}})}}}{4}},}
ctg
7
π
60
=
tg
23
π
60
=
ctg
21
∘
=
tg
69
∘
=
2
(
2
(
5
−
2
)
+
3
(
3
−
5
)
)
+
(
3
(
5
+
1
)
+
2
)
2
(
25
−
11
5
)
4
,
{\displaystyle \operatorname {ctg} {\frac {7\,\pi }{60}}=\operatorname {tg} {\frac {23\,\pi }{60}}=\operatorname {ctg} 21^{\circ }=\operatorname {tg} 69^{\circ }={\frac {2(2({\sqrt {5}}-2)+{\sqrt {3}}(3-{\sqrt {5}}))+({\sqrt {3}}({\sqrt {5}}+1)+2){\sqrt {2(25-11{\sqrt {5}})}}}{4}},}
sin
2
π
15
=
cos
11
π
30
=
sin
24
∘
=
cos
66
∘
=
3
(
5
+
1
)
−
2
(
5
−
5
)
8
,
{\displaystyle \sin {\frac {2\,\pi }{15}}=\cos {\frac {11\,\pi }{30}}=\sin 24^{\circ }=\cos 66^{\circ }={\frac {{\sqrt {3}}({\sqrt {5}}+1)-{\sqrt {2(5-{\sqrt {5}})}}}{8}},}
cos
2
π
15
=
sin
11
π
30
=
cos
24
∘
=
sin
66
∘
=
5
+
1
+
6
(
5
−
5
)
8
,
{\displaystyle \cos {\frac {2\,\pi }{15}}=\sin {\frac {11\,\pi }{30}}=\cos 24^{\circ }=\sin 66^{\circ }={\frac {{\sqrt {5}}+1+{\sqrt {6(5-{\sqrt {5}})}}}{8}},}
tg
2
π
15
=
ctg
11
π
30
=
tg
24
∘
=
ctg
66
∘
=
−
3
(
3
+
5
)
+
2
(
25
+
11
5
)
2
,
{\displaystyle \operatorname {tg} {\frac {2\,\pi }{15}}=\operatorname {ctg} {\frac {11\,\pi }{30}}=\operatorname {tg} 24^{\circ }=\operatorname {ctg} 66^{\circ }={\frac {-{\sqrt {3}}(3+{\sqrt {5}})+{\sqrt {2(25+11{\sqrt {5}})}}}{2}},}
ctg
2
π
15
=
tg
11
π
30
=
ctg
24
∘
=
tg
66
∘
=
3
(
5
−
1
)
+
2
(
5
−
5
)
2
,
{\displaystyle \operatorname {ctg} {\frac {2\,\pi }{15}}=\operatorname {tg} {\frac {11\,\pi }{30}}=\operatorname {ctg} 24^{\circ }=\operatorname {tg} 66^{\circ }={\frac {{\sqrt {3}}({\sqrt {5}}-1)+{\sqrt {2(5-{\sqrt {5}})}}}{2}},}
sin
3
π
20
=
cos
7
π
20
=
sin
27
∘
=
cos
63
∘
=
−
2
(
5
−
1
)
+
2
5
+
5
8
,
{\displaystyle \sin {\frac {3\,\pi }{20}}=\cos {\frac {7\,\pi }{20}}=\sin 27^{\circ }=\cos 63^{\circ }={\frac {-{\sqrt {2}}({\sqrt {5}}-1)+2{\sqrt {5+{\sqrt {5}}}}}{8}},}
cos
3
π
20
=
sin
7
π
20
=
cos
27
∘
=
sin
63
∘
=
2
(
5
−
1
)
+
2
5
+
5
8
,
{\displaystyle \cos {\frac {3\,\pi }{20}}=\sin {\frac {7\,\pi }{20}}=\cos 27^{\circ }=\sin 63^{\circ }={\frac {{\sqrt {2}}({\sqrt {5}}-1)+2{\sqrt {5+{\sqrt {5}}}}}{8}},}
tg
3
π
20
=
ctg
7
π
20
=
tg
27
∘
=
ctg
63
∘
=
5
−
1
−
5
−
2
5
,
{\displaystyle \operatorname {tg} {\frac {3\,\pi }{20}}=\operatorname {ctg} {\frac {7\,\pi }{20}}=\operatorname {tg} 27^{\circ }=\operatorname {ctg} 63^{\circ }={{\sqrt {5}}-1-{\sqrt {5-2{\sqrt {5}}}}},}
ctg
3
π
20
=
tg
7
π
20
=
ctg
27
∘
=
tg
63
∘
=
5
−
1
+
5
−
2
5
,
{\displaystyle \operatorname {ctg} {\frac {3\,\pi }{20}}=\operatorname {tg} {\frac {7\,\pi }{20}}=\operatorname {ctg} 27^{\circ }=\operatorname {tg} 63^{\circ }={{\sqrt {5}}-1+{\sqrt {5-2{\sqrt {5}}}}},}
sin
11
π
60
=
cos
19
π
60
=
sin
33
∘
=
cos
57
∘
=
2
(
3
+
1
)
(
5
−
1
)
+
2
(
3
−
1
)
5
+
5
16
,
{\displaystyle \sin {\frac {11\,\pi }{60}}=\cos {\frac {19\,\pi }{60}}=\sin 33^{\circ }=\cos 57^{\circ }={\frac {{\sqrt {2}}({\sqrt {3}}+1)({\sqrt {5}}-1)+2({\sqrt {3}}-1){\sqrt {5+{\sqrt {5}}}}}{16}},}
cos
11
π
60
=
sin
19
π
60
=
cos
33
∘
=
sin
57
∘
=
−
2
(
3
−
1
)
(
5
−
1
)
+
2
(
3
+
1
)
5
+
5
16
,
{\displaystyle \cos {\frac {11\,\pi }{60}}=\sin {\frac {19\,\pi }{60}}=\cos 33^{\circ }=\sin 57^{\circ }={\frac {-{\sqrt {2}}({\sqrt {3}}-1)({\sqrt {5}}-1)+2({\sqrt {3}}+1){\sqrt {5+{\sqrt {5}}}}}{16}},}
tg
11
π
60
=
ctg
19
π
60
=
tg
33
∘
=
ctg
57
∘
=
−
2
(
5
+
2
)
+
3
(
3
+
5
)
+
(
2
−
3
)
(
3
(
5
+
1
)
−
2
)
5
−
2
5
2
,
{\displaystyle \operatorname {tg} {\frac {11\,\pi }{60}}=\operatorname {ctg} {\frac {19\,\pi }{60}}=\operatorname {tg} 33^{\circ }=\operatorname {ctg} 57^{\circ }={\frac {-2({\sqrt {5}}+2)+{\sqrt {3}}(3+{\sqrt {5}})+(2-{\sqrt {3}})({\sqrt {3}}({\sqrt {5}}+1)-2){\sqrt {5-2{\sqrt {5}}}}}{2}},}
ctg
11
π
60
=
tg
19
π
60
=
ctg
33
∘
=
tg
57
∘
=
−
2
(
2
(
5
+
2
)
+
3
(
3
+
5
)
)
+
(
3
(
5
−
1
)
+
2
)
2
(
25
+
11
5
)
4
,
{\displaystyle \operatorname {ctg} {\frac {11\,\pi }{60}}=\operatorname {tg} {\frac {19\,\pi }{60}}=\operatorname {ctg} 33^{\circ }=\operatorname {tg} 57^{\circ }={\frac {-2(2({\sqrt {5}}+2)+{\sqrt {3}}(3+{\sqrt {5}}))+({\sqrt {3}}({\sqrt {5}}-1)+2){\sqrt {2(25+11{\sqrt {5}})}}}{4}},}
sin
13
π
60
=
cos
17
π
60
=
sin
39
∘
=
cos
51
∘
=
2
(
3
+
1
)
(
5
+
1
)
−
2
(
3
−
1
)
5
−
5
16
,
{\displaystyle \sin {\frac {13\,\pi }{60}}=\cos {\frac {17\,\pi }{60}}=\sin 39^{\circ }=\cos 51^{\circ }={\frac {{\sqrt {2}}({\sqrt {3}}+1)({\sqrt {5}}+1)-2({\sqrt {3}}-1){\sqrt {5-{\sqrt {5}}}}}{16}},}
cos
13
π
60
=
sin
17
π
60
=
cos
39
∘
=
sin
51
∘
=
2
(
3
−
1
)
(
5
+
1
)
+
2
(
3
+
1
)
5
−
5
16
,
{\displaystyle \cos {\frac {13\,\pi }{60}}=\sin {\frac {17\,\pi }{60}}=\cos 39^{\circ }=\sin 51^{\circ }={\frac {{\sqrt {2}}({\sqrt {3}}-1)({\sqrt {5}}+1)+2({\sqrt {3}}+1){\sqrt {5-{\sqrt {5}}}}}{16}},}
tg
13
π
60
=
ctg
17
π
60
=
tg
39
∘
=
ctg
51
∘
=
−
2
(
2
(
5
−
2
)
+
3
(
3
−
5
)
)
+
(
3
(
5
+
1
)
+
2
)
2
(
25
−
11
5
)
4
,
{\displaystyle \operatorname {tg} {\frac {13\,\pi }{60}}=\operatorname {ctg} {\frac {17\,\pi }{60}}=\operatorname {tg} 39^{\circ }=\operatorname {ctg} 51^{\circ }={\frac {-2(2({\sqrt {5}}-2)+{\sqrt {3}}(3-{\sqrt {5}}))+({\sqrt {3}}({\sqrt {5}}+1)+2){\sqrt {2(25-11{\sqrt {5}})}}}{4}},}
ctg
13
π
60
=
tg
17
π
60
=
ctg
39
∘
=
tg
51
∘
=
−
2
(
2
(
5
−
2
)
−
3
(
3
−
5
)
)
+
(
3
(
5
+
1
)
−
2
)
2
(
25
−
11
5
)
4
,
{\displaystyle \operatorname {ctg} {\frac {13\,\pi }{60}}=\operatorname {tg} {\frac {17\,\pi }{60}}=\operatorname {ctg} 39^{\circ }=\operatorname {tg} 51^{\circ }={\frac {-2(2({\sqrt {5}}-2)-{\sqrt {3}}(3-{\sqrt {5}}))+({\sqrt {3}}({\sqrt {5}}+1)-2){\sqrt {2(25-11{\sqrt {5}})}}}{4}},}
sin
7
π
30
=
cos
8
π
30
=
sin
42
∘
=
cos
48
∘
=
−
(
5
−
1
)
+
6
(
5
+
5
)
8
,
{\displaystyle \sin {\frac {7\,\pi }{30}}=\cos {\frac {8\,\pi }{30}}=\sin 42^{\circ }=\cos 48^{\circ }={\frac {-({\sqrt {5}}-1)+{\sqrt {6(5+{\sqrt {5}})}}}{8}},}
cos
7
π
30
=
sin
8
π
30
=
cos
42
∘
=
sin
48
∘
=
3
(
5
−
1
)
+
2
(
5
+
5
)
8
,
{\displaystyle \cos {\frac {7\,\pi }{30}}=\sin {\frac {8\,\pi }{30}}=\cos 42^{\circ }=\sin 48^{\circ }={\frac {{\sqrt {3}}({\sqrt {5}}-1)+{\sqrt {2(5+{\sqrt {5}})}}}{8}},}
tg
7
π
30
=
ctg
8
π
30
=
tg
42
∘
=
ctg
48
∘
=
3
(
5
+
1
)
−
2
(
5
+
5
)
2
,
{\displaystyle \operatorname {tg} {\frac {7\,\pi }{30}}=\operatorname {ctg} {\frac {8\,\pi }{30}}=\operatorname {tg} 42^{\circ }=\operatorname {ctg} 48^{\circ }={\frac {{\sqrt {3}}({\sqrt {5}}+1)-{\sqrt {2(5+{\sqrt {5}})}}}{2}},}
ctg
7
π
30
=
tg
8
π
30
=
ctg
42
∘
=
tg
48
∘
=
3
(
3
−
5
)
+
2
(
25
−
11
5
)
2
,
{\displaystyle \operatorname {ctg} {\frac {7\,\pi }{30}}=\operatorname {tg} {\frac {8\,\pi }{30}}=\operatorname {ctg} 42^{\circ }=\operatorname {tg} 48^{\circ }={\frac {{\sqrt {3}}(3-{\sqrt {5}})+{\sqrt {2(25-11{\sqrt {5}})}}}{2}},}
tg
π
120
=
ctg
59
π
120
=
tg
1.5
∘
=
ctg
88.5
∘
=
8
−
2
(
2
−
3
)
(
3
−
5
)
−
2
(
2
+
3
)
(
5
+
5
)
8
+
2
(
2
−
3
)
(
3
−
5
)
+
2
(
2
+
3
)
(
5
+
5
)
,
{\displaystyle \operatorname {tg} {\frac {\pi }{120}}=\operatorname {ctg} {\frac {59\,\pi }{120}}=\operatorname {tg} 1.5^{\circ }=\operatorname {ctg} 88.5^{\circ }={\sqrt {\frac {8-{\sqrt {2(2-{\sqrt {3}})(3-{\sqrt {5}})}}-{\sqrt {2(2+{\sqrt {3}})(5+{\sqrt {5}})}}}{8+{\sqrt {2(2-{\sqrt {3}})(3-{\sqrt {5}})}}+{\sqrt {2(2+{\sqrt {3}})(5+{\sqrt {5}})}}}}},}
cos
π
240
=
sin
119
π
240
=
cos
0.75
∘
=
sin
89.25
∘
=
1
16
(
2
−
2
+
2
(
2
(
5
+
5
)
+
3
(
1
−
5
)
)
+
{\displaystyle \cos {\frac {\pi }{240}}=\sin {\frac {119\,\pi }{240}}=\cos 0.75^{\circ }=\sin 89.25^{\circ }={\frac {1}{16}}\left({\sqrt {2-{\sqrt {2+{\sqrt {2}}}}}}\left({\sqrt {2(5+{\sqrt {5}})}}+{\sqrt {3}}(1-{\sqrt {5}})\right)+\right.}
+
2
+
2
+
2
(
6
(
5
+
5
)
+
5
−
1
)
)
,
{\displaystyle \left.+{\sqrt {2+{\sqrt {2+{\sqrt {2}}}}}}\left({\sqrt {6(5+{\sqrt {5}})}}+{\sqrt {5}}-1\right)\right),}
cos
π
17
=
sin
15
π
34
=
1
8
2
(
2
3
17
−
2
(
85
+
19
17
)
+
17
+
2
(
17
−
17
)
+
17
+
15
)
.
{\displaystyle \cos {\frac {\pi }{17}}=\sin {\frac {15\,\pi }{34}}={\frac {1}{8}}{\sqrt {2\left(2{\sqrt {3{\sqrt {17}}-{\sqrt {2(85+19{\sqrt {17}})}}+17}}+{\sqrt {2(17-{\sqrt {17}})}}+{\sqrt {17}}+15\right)}}.}
