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Baltic Way
1994 Baltic Way
3
Begging for trig substitution
Begging for trig substitution
Source: Baltic Way 1994
December 22, 2011
trigonometry
inequalities proposed
inequalities
Problem Statement
Find the largest value of the expression
x
y
+
x
1
−
x
2
+
y
1
−
y
2
−
(
1
−
x
2
)
(
1
−
y
2
)
xy+x\sqrt{1-x^2}+y\sqrt{1-y^2}-\sqrt{(1-x^2)(1-y^2)}
x
y
+
x
1
−
x
2
+
y
1
−
y
2
−
(
1
−
x
2
)
(
1
−
y
2
)
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