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15
2013 PUMaC Team 15
2013 PUMaC Team 15
Source:
November 24, 2013
trigonometry
inequalities
induction
Problem Statement
Prove:
∣
sin
a
1
∣
+
∣
sin
a
2
∣
+
∣
sin
a
3
∣
+
…
+
∣
sin
a
n
∣
+
∣
cos
(
a
1
+
a
2
+
a
3
+
…
+
a
n
)
∣
≥
1.
|\sin a_1|+|\sin a_2|+|\sin a_3|+\ldots+|\sin a_n|+|\cos(a_1+a_2+a_3+\ldots+a_n)|\geq 1.
∣
sin
a
1
∣
+
∣
sin
a
2
∣
+
∣
sin
a
3
∣
+
…
+
∣
sin
a
n
∣
+
∣
cos
(
a
1
+
a
2
+
a
3
+
…
+
a
n
)
∣
≥
1.
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