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\usepackage[utf8]{inputenc}
\usepackage{fontspec}
\usepackage{amsmath, amsfonts, amssymb, amsthm}
\usepackage{graphicx}
\usepackage{xcolor}
\usepackage{multicol}
\usepackage{enumitem}
\usepackage{mathrsfs}
\usepackage{colortbl}
\usepackage{varwidth}
\usepackage[most]{tcolorbox}


\tcbuselibrary{skins,breakable}
\usepackage{tikz,tkz-euclide}
\usetikzlibrary{calc}
\usetikzlibrary{shadows}
\usepackage{tabularx, array, booktabs}
\usepackage{setspace}
\usepackage{hyperref}
\hypersetup{
    colorlinks=true,
    urlcolor=magenta
}

\usepackage{fancyhdr}

% French language support
\usepackage[french]{babel}

% Bottom message in Arabic requires bidi package
\usepackage{bidi}
\newfontfamily\arabicfont[Script=Arabic,Scale=1.1]{Amiri}

% Two-page layout (conditionally included)



% --- Colors ---
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\definecolor{pBlue}{RGB}{102, 53, 153}

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\definecolor{lightgray}{gray}{0.6}
\definecolor{arrowblue}{RGB}{0,140,180}
\definecolor{bannerblue}{RGB}{210,240,240}

% --- Basic Settings ---
% Language variables for French exams
\def\professor{R. MOSAID}  % Should be R. MOSAID not {{R. MOSAID}}
\def\classname{TCSF}
\def\examtitle{Devoir 01 - S02 \circled{D}}
\def\schoolname{Taghzirt}
\def\academicyear{2025/2026}
\def\subject{Mathématiques}
\def\duration{2h}
\def\secondtitle{\small{visit ~~\wsite~~ for more!}}
\def\province{Direction provinciale\newline de Beni Mellal}
\def\logo{\includegraphics[width=\linewidth]{images/logo-men.png}}
\def\wsite{\href{https://www.mosaid.xyz}{\textcolor{magenta}{\texttt{www.mosaid.xyz}}}}
\def\ddate{\hfill \number\day/\number\month/\number\year~~}


% Exam-specific settings and custom definitions
% This file is generated in the current working directory
% Edit this file to customize your exam settings



% Define column type for centered cells
\newcolumntype{Y}{>{\centering\arraybackslash}X}
\newcolumntype{M}[1]{@{}>{\centering\arraybackslash}m{#1}@{}}

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\newcommand{\circled}[1]{%
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    \node[shape=circle,draw,inner sep=1pt, font=\bf] (char) {#1};}%
}


% --- Margin offsets for note placement ---
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\def\lnotemargin{1.5}   % distance from left edge of text block


% --- Note number placed 1cm from page edge (right margin) ---
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    \node[anchor=base west,
      font=\scriptsize\bfseries,
      fill=yellow!30,
      draw=black,
      circle,
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% --- Note number placed 1cm from page edge (left margin) ---
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% Document spacing
\setstretch{1.7}

% Math display style
\everymath{\displaystyle}

\mathversion{bold}

\AtBeginDocument{\fontsize{13}{15}\selectfont}

%\newcommand{\fff}[1]{\makebox[#1cm]{\dotfill}}

\newcommand{\dfp}[1]{\dotfill (\bf{#1 pt})}

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% Custom theorem environments (uncomment if needed)
% \newtheorem{theorem}{Theorem}
% \newtheorem{lemma}{Lemma}
% \newtheorem{corollary}{Corollary}

% Custom exercise environments (uncomment if needed)
% \newenvironment{solution}{\begin{proof}[Solution]}{\end{proof}}
% \newenvironment{remark}{\begin{proof}[Remark]}{\end{proof}}

% Custom commands for this exam (add your own below)
% \newcommand{\answerline}[1]{\underline{\hspace{#1}}}
% \newcommand{\points}[1]{\hfill(\mbox{#1 points})}

% Additional packages (uncomment if needed)
% \usepackage{siunitx} % For SI units
% \usepackage{chemformula} % For chemical formulas
% \usepackage{circuitikz} % For circuit diagrams

% Page layout adjustments
% \setlength{\parindent}{0pt}
% \setlength{\parskip}{1em}

% Custom colors for this exam
% \definecolor{myblue}{RGB}{0,100,200}
% \definecolor{mygreen}{RGB}{0,150,0}

% ----------------------------------------------------------------------
% ADD YOUR CUSTOM DEFINITIONS BELOW THIS LINE
% ----------------------------------------------------------------------

% Example:
\newcommand{\dif}{\mathrm{d}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\C}{\mathbb{C}}


% Exercise Theme 1: TikZ shadow title
\newcommand{\exothemeone}[1]{%
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}

\newcommand{\printexo}[3]{%
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    \def\fulltitle{Exercice #1}%
  \else
    \def\fulltitle{Exercice #1~#2}%
  \fi
  \exothemeone{\fulltitle}%
  \noindent #3%
  \vspace{0.2cm}%
}

% --- Header Style 9 (fr)  ---
\newcommand{\printheadnine}{%
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      M{0.25\textwidth}
      M{0.48\textwidth}
      M{0.25\textwidth}
      }
      \textbf{\classname} & \textbf{\examtitle} & \ddate \\
      \wsite & \secondtitle & \hfill \begin{tabular}{|c|}\hline\professor\end{tabular}  \\
      \hline
  \end{tabularx}
  \arrayrulecolor{black}
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\setlength{\headheight}{47pt}
\setlength{\headsep}{0pt}
\fancyhead[C]{%
  \printheadnine
}%
\pagestyle{fancy}




\begin{document}




\VMargin{1.85cm}
\vspace*{-0.75cm}
% Exercise 1 (originally 1)
\printexo{1}{: ~ (5 points)}{
\vspace*{-1cm}
\begin{enumerate}
  \item \note{1} Déterminer l’abscisse curviligne principale du point $A\left(\frac{2029\pi}{3}\right)$\\
  \item \note{3} Placer les points $A$, $B\left(\frac{7\pi}{6}\right)$ et le point $C$ tel que
    $\left(\overline{\overrightarrow{OB},\overrightarrow{OC}}\right)\equiv \frac{5\pi}{4}\,[2\pi]$
  \item \note{1} Déterminer l’abscisse curviligne principale du point $C$
\end{enumerate}
}

% Exercise 2 (originally 2)
\printexo{2}{: ~ (5.5 points)}{
\vspace*{-1cm}
\begin{enumerate}
  \item \note{4} Simplifier les expressions suivantes.\\
        \(A = 2\sin(x-5\pi) - 3\cos\left(4\pi+x\right) + \sin\left(\frac{7\pi}{2}+x\right),\)\\
        \(B = \cos\left(\frac{\pi}{12}\right) + \cos\left(\frac{5\pi}{12}\right) + \cos\left(\frac{7\pi}{12}\right) + \cos\left(\frac{11\pi}{12}\right).\)
  \item \note{1.5} Sachant que  \(\sin \frac{7\pi}{8} = \frac{\sqrt{2-\sqrt2}}{2}\).
    Calculer \(\cos \frac{7\pi}{8} \).
\end{enumerate}
}

% Exercise 3 (originally 3)
\printexo{3}{: ~ (10.5 points)}{
Soit l'intervalle \(I = \left]-\pi;-\frac{\pi}{2}\right[\cup\left]\frac{\pi}{2};\pi\right[\).
Pour tout ~$x\in I$~ On pose :
\[f(x) = 2\sin x - 2\cos x + \sqrt{3}\tan x - \sqrt3.\]
\begin{enumerate}[label=\arabic*.]
    \item
        \begin{enumerate}[label=\alph*.]
            \item \note{1} Vérifier que \(f(x) = (2\cos x + \sqrt3)(\tan x - 1)\).
            \item \note{1.5} Calculer : \(f\left(\frac{\pi}{4}\right),\quad f(\pi)\quad\text{et}\quad f\left(\frac{5\pi}{6}\right)\).
        \end{enumerate}
    \item
        \begin{enumerate}[label=\alph*.]
            \item \note{3} Résoudre dans \(I\) les équations :
                \(2\cos x + \sqrt3 = 0 \quad\text{et}\quad \tan x - 1 = 0.\)
            \item \note{0.5} En déduire dans \(I\) les solutions de \(f(x)=0\).
        \end{enumerate}
    \item
        \begin{enumerate}[label=\alph*.]
            \item \note{3} Résoudre dans \(I\) les inéquations :
                \(2\cos x + \sqrt3 > 0 \quad\text{et}\quad \tan x - 1 \le 0.\)
            \item \note{1} Donner le tableau de signe de \(f(x)\) sur \(I\).
            \item \note{0.5} En déduire dans \(I\) les solutions de l’inéquation \(f(x) < 0\).
        \end{enumerate}
\end{enumerate}
}






% Bottom message
\begin{center}
  \normalsize{%
    \vskip 3pt \hrule height 3pt \vskip 5pt
    \RL{\arabicfont
    ﴿فَلِلَّهِ ٱلْحَمْدُ رَبِّ ٱلسَّمَـٰوَٰتِ وَرَبِّ ٱلْأَرْضِ رَبِّ ٱلْعَـٰلَمِينَ (36)•  وَلَهُ ٱلْكِبْرِيَآءُ فِى ٱلسَّمَـٰوَٰتِ وَٱلْأَرْضِ ۖ وَهُوَ ٱلْعَزِيزُ ٱلْحَكِيمُ (37)• ﴾ (الجاثية الآيات 36-37)
    }%
  }%
\end{center}

\end{document}