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Soros Olympiad in Mathematics
V Soros Olympiad 1998 - 99 (Russia)
10.2
draw cos(x + y)^2 <= cos(x - y)^2 (V Soros Olympiad 1998-99 Round 1 10.2)
draw cos(x + y)^2 <= cos(x - y)^2 (V Soros Olympiad 1998-99 Round 1 10.2)
Source:
May 25, 2024
trigonometry
analytic geometry
Problem Statement
On the coordinate plane, draw all points
M
(
x
,
y
)
M(x, y)
M
(
x
,
y
)
, the coordinates of which satisfy the inequalities
cos
(
x
+
y
)
2
≤
cos
(
x
−
y
)
2
,
0
≤
x
3
,
0
≤
y
3
.
\cos(x + y)^2 \le \cos(x - y)^2, \,\,\, 0 \le x^3, \,\,\, 0 \le y^3.
cos
(
x
+
y
)
2
≤
cos
(
x
−
y
)
2
,
0
≤
x
3
,
0
≤
y
3
.
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