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Soros Olympiad in Mathematics
III Soros Olympiad 1996 - 97 (Russia)
11.8
2x2 trig. system (III Soros Olympiad 1996-97 R3 11.8)
2x2 trig. system (III Soros Olympiad 1996-97 R3 11.8)
Source:
May 31, 2024
algebra
trigonometry
system of equations
Problem Statement
Solve the system of equations:
2
(
3
−
2
cos
y
)
2
+
2
(
4
−
2
sin
y
)
2
=
2
(
3
−
x
)
2
+
32
=
(
x
−
2
cos
y
)
2
+
4
sin
2
y
2(3-2\cos y)^2+2(4-2\sin y)^2=2(3-x)^2+32=(x-2\cos y)^2+4\sin^2y
2
(
3
−
2
cos
y
)
2
+
2
(
4
−
2
sin
y
)
2
=
2
(
3
−
x
)
2
+
32
=
(
x
−
2
cos
y
)
2
+
4
sin
2
y
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