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2017 Latvia Baltic Way TST
2
(x+y)(2- sin(x+y)/ 4 sin^2(x+y)=xy/(x+y)
(x+y)(2- sin(x+y)/ 4 sin^2(x+y)=xy/(x+y)
Source: 2017 Latvia BW TST P2
December 18, 2022
algebra
equation
trigonometry
Trigonometric Equations
Problem Statement
Find all pairs of real numbers
(
x
,
y
)
(x, y)
(
x
,
y
)
that satisfy the equation
(
x
+
y
)
(
2
−
sin
(
x
+
y
)
)
4
sin
2
(
x
+
y
)
=
x
y
x
+
y
\frac{(x+y)(2-\sin(x+y))}{4\sin^2(x+y)}=\frac{xy}{x+y}
4
sin
2
(
x
+
y
)
(
x
+
y
)
(
2
−
sin
(
x
+
y
))
=
x
+
y
x
y
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