Art of Problem Solving

2020 AMC 12A Problems/Problem 9: Difference between revisions

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==Problem 9==
==Problem==


How many solutions does the equation tan<math>(2x)=cos(\frac{x}{2})</math> have on the interval <math>[0,2\pi]?</math>
How many solutions does the equation tan<math>(2x)=cos(\frac{x}{2})</math> have on the interval <math>[0,2\pi]?</math>


<math> \textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5 </math>
<math> \textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5 </math>

Revision as of 13:08, 1 February 2020

Problem

How many solutions does the equation tan$(2x)=cos(\frac{x}{2})$ have on the interval $[0,2\pi]?$

$\textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5$