MathDB
Weird DeMoivre Stuff

Source: 2023 AMC 12A P25

November 9, 2023
AMCAMC 12trigonometry2023 AMC2023 AMC 12ASequences

Problem Statement

There is a unique sequence of integers a1,a2,⋯a2023a_1, a_2, \cdots a_{2023} such that tan⁡2023x=a1tan⁡x+a3tan⁡3x+a5tan⁡5x+⋯+a2023tan⁡2023x1+a2tan⁡2x+a4tan⁡4x⋯+a2022tan⁡2022x \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\tan 2023x is defined. What is a2023?a_{2023}?
<spanclass=′latex−bold′>(A)</span>−2023<spanclass=′latex−bold′>(B)</span>−2022<spanclass=′latex−bold′>(C)</span>−1<spanclass=′latex−bold′>(D)</span>1<spanclass=′latex−bold′>(E)</span>2023<span class='latex-bold'>(A) </span> -2023 \qquad<span class='latex-bold'>(B) </span> -2022 \qquad<span class='latex-bold'>(C) </span> -1 \qquad<span class='latex-bold'>(D) </span> 1 \qquad<span class='latex-bold'>(E) </span> 2023
Back to ProblemsView on AoPS