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1/ sin^2 b, 1/cos^2 b, integer roots of x^2-ax+a=0 - 1985 Greece MO X p1
1/ sin^2 b, 1/cos^2 b, integer roots of x^2-ax+a=0 - 1985 Greece MO X p1
Source:
September 8, 2024
algebra
trigonometry
Problem Statement
Find all arcs
θ
\theta
θ
such that
1
sin
2
θ
,
1
cos
2
θ
\frac{1}{\sin ^2 \theta}, \frac{1}{\cos ^2 \theta}
s
i
n
2
θ
1
,
c
o
s
2
θ
1
are integer numbers and roots of equation
x
2
−
a
x
+
a
=
0.
x^2-ax+a=0.
x
2
−
a
x
+
a
=
0.
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