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2020 LMT Spring
24
Spring 2020 Team Round Problem 24
Spring 2020 Team Round Problem 24
Source:
August 22, 2020
Problem Statement
Let
a
a
a
,
b
b
b
, and
c
c
c
be real angles such that \newline
3
sin
a
+
4
sin
b
+
5
sin
c
=
0
3\sin a + 4\sin b + 5\sin c = 0
3
sin
a
+
4
sin
b
+
5
sin
c
=
0
3
cos
a
+
4
cos
b
+
5
cos
c
=
0.
3\cos a + 4\cos b + 5\cos c = 0.
3
cos
a
+
4
cos
b
+
5
cos
c
=
0.
\newline The maximum value of the expression
sin
b
sin
c
sin
2
a
\frac{\sin b \sin c}{\sin^2 a}
s
i
n
2
a
s
i
n
b
s
i
n
c
can be expressed as
p
q
\frac{p}{q}
q
p
for relatively prime
p
,
q
p,q
p
,
q
. Compute
p
+
q
p+q
p
+
q
.
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