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2004 All-Russian Olympiad Regional Round
10.1
cosa+cosb+cosc>sina+sinb+sinc- All-Russian MO 2004 Regional (R4) 10.1
cosa+cosb+cosc>sina+sinb+sinc- All-Russian MO 2004 Regional (R4) 10.1
Source:
September 27, 2024
trigonometry
algebra
inequalities
Problem Statement
The sum of positive numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
is equal to
π
/
2
\pi/2
π
/2
. Prove that
cos
a
+
cos
b
+
cos
c
>
sin
a
+
sin
b
+
sin
c
.
\cos a + \cos b + \cos c > \sin a + \sin b + \sin c.
cos
a
+
cos
b
+
cos
c
>
sin
a
+
sin
b
+
sin
c
.
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