2023 AMC 12A Problems/Problem 25

Problem

There is a unique sequence of integers $a_1, a_2, \cdots a_{2023}$ such that $\tan2023x = \frac{a_1 \tan x + a_3 \tan^3 x + a_5 \tan^5 x + \cdots + a_{2023} \tan^{2023} x}{1 + a_2 \tan^2 x + a_4 \tan^4 x \cdots + a_{2022} \tan^{2022} x}$ whenever $\tan 2023x$ is defined. What is $a_{2023}?$

$\textbf{(A) } -2023 \qquad\textbf{(B) } -2022 \qquad\textbf{(C) } -1 \qquad\textbf{(D) } 1 \qquad\textbf{(E) } 2023$

Solution

2023 AMC 12A (Problems • Answer Key • Resources)
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All AMC 12 Problems and Solutions

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2023 AMC 12A Problems/Problem 25

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