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2021 MMATHS
11
MMATHS 2021, Problem 11: Trig Product
MMATHS 2021, Problem 11: Trig Product
Source:
October 31, 2021
Yale
MMATHS
Problem Statement
If
∏
i
=
6
2021
(
1
−
tan
2
(
(
2
i
)
∘
)
)
\displaystyle\prod_{i=6}^{2021} (1-\tan^2((2^i)^\circ))
i
=
6
∏
2021
(
1
−
tan
2
((
2
i
)
∘
))
can be written in the form
a
b
a^b
a
b
for positive integers
a
,
b
a,b
a
,
b
with
a
a
a
squarefree, find
a
+
b
a+b
a
+
b
.Proposed by Deyuan Li and Andrew Milas
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