MathDB
Problems
Contests
National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2018 India PRMO
14
14
Part of
2018 India PRMO
Problems
(1)
2018 preRMO p14, x=cos1cos2cos3..·cos89, y=cos2cos6cos10...cos86
Source:
8/8/2019
If
x
=
c
o
s
1
o
c
o
s
2
o
c
o
s
3
o
.
.
.
c
o
s
8
9
o
x = cos 1^o cos 2^o cos 3^o...cos 89^o
x
=
cos
1
o
cos
2
o
cos
3
o
...
cos
8
9
o
and
y
=
c
o
s
2
o
c
o
s
6
o
c
o
s
1
0
o
.
.
.
c
o
s
8
6
o
y = cos 2^o cos 6^o cos 10^o...cos 86^o
y
=
cos
2
o
cos
6
o
cos
1
0
o
...
cos
8
6
o
, then what is the integer nearest to
2
7
log
2
y
x
\frac27 \log_2 \frac{y}{x}
7
2
lo
g
2
x
y
?
trigonometry
logarithms