MathDB
Problems
Contests
National and Regional Contests
Ireland Contests
Ireland National Math Olympiad
1988 Irish Math Olympiad
12
Irish 1988 paper 1 #12
Irish 1988 paper 1 #12
Source:
September 7, 2014
trigonometry
Problem Statement
Prove that if
n
n
n
is a positive integer ,then
c
o
s
4
π
2
n
+
1
+
c
o
s
4
2
π
2
n
+
1
+
⋯
+
c
o
s
4
n
π
2
n
+
1
=
6
n
−
5
16
.
cos^4\frac{\pi}{2n+1}+cos^4\frac{2\pi}{2n+1}+\cdots+cos^4\frac{n\pi}{2n+1}=\frac{6n-5}{16}.
co
s
4
2
n
+
1
π
+
co
s
4
2
n
+
1
2
π
+
⋯
+
co
s
4
2
n
+
1
nπ
=
16
6
n
−
5
.
Back to Problems
View on AoPS