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Saint Petersburg Mathematical Olympiad
2021 Saint Petersburg Mathematical Olympiad
1
Solve trigonometric system of equations
Solve trigonometric system of equations
Source: St Petersburg 2021 10.1
December 23, 2021
algebra
system of equations
Problem Statement
Solve the following system of equations
sin
2
x
+
cos
2
y
=
y
4
.
\sin^2{x} + \cos^2{y} = y^4.
sin
2
x
+
cos
2
y
=
y
4
.
sin
2
y
+
cos
2
x
=
x
2
.
\sin^2{y} + \cos^2{x} = x^2.
sin
2
y
+
cos
2
x
=
x
2
.
A. Khrabov
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