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Problems
Problem
Problem
Statement I
If in a triangle ABC
sin
2
A
+
sin
2
B
+
sin
2
C
=
2
\sin^2 A + \sin^2 B + \sin^2 C = 2
sin
2
A
+
sin
2
B
+
sin
2
C
=
2
, then one of the angles must be
90
∘
90^\circ
9
0
∘
.
Statement II
In any triangles ABC
cos
2
A
+
cos
2
B
+
cos
2
C
=
−
1
−
4
cos
A
cos
B
cos
C
\cos 2A + \cos 2B + \cos 2C = -1 - 4 \cos A \cos B \cos C
cos
2
A
+
cos
2
B
+
cos
2
C
=
−
1
−
4
cos
A
cos
B
cos
C
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