\documentclass[a4paper,12pt]{article}

\usepackage[left=2.50cm, right=1.00cm, top=2cm, bottom=1.50cm]{geometry}

\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 ---
\definecolor{maroon}{cmyk}{0,0.87,0.68,0.32}
\definecolor{pBlue}{RGB}{102, 53, 153}

\definecolor{myblue}{HTML}{1D2A6E}
\definecolor{myred}{HTML}{A97E77}
\definecolor{mybrown}{HTML}{B35823}
\definecolor{gold}{HTML}{B48920}
\definecolor{myorange}{HTML}{ED8C2B}
\definecolor{col}{RGB}{45, 136, 119}
\definecolor{MainRed}{rgb}{.8, .1, .1}
\definecolor{winered}{rgb}{0.5,0,0}
\definecolor{JungleGreen}{HTML}{29AB87}

\definecolor{myblue3}{RGB}{36, 57, 126}
\definecolor{mygray}{RGB}{112,121,139}
\definecolor{LemonGlacier}{RGB}{253,255,0}
\colorlet{myblue3}{red!75!black}

\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{A}}
\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}@{}}

\newcommand{\tb}{\tikz[baseline=-0.6ex]{\fill (0,0) circle (2pt);}~}

\newcommand{\ccc}[1]{
    \begin{tikzpicture}[overlay, remember picture]
        \node[circle, inner sep=3pt, draw=black, outer sep=0pt] at (0.5,0.2) {#1};
    \end{tikzpicture}
}


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


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


% --- Note number placed 1cm from page edge (right margin) ---
\newcommand{\rnote}[1]{%
  \tikz[remember picture,overlay,baseline=(text.base)]{%
    % a tiny anchor at the current line baseline
    \node (text) at (0,0) {};%
    % coordinate 1cm left of the physical page right edge
    \coordinate (marg) at ($(current page.east)+(\rnotemargin,0)$);%
    % place the marker using x from 'marg' and y from 'text.base'
    \node[anchor=base west,
      font=\scriptsize\bfseries,
      fill=yellow!30,
      draw=black,
      circle,
      minimum size=14pt,
      inner sep=1pt
    ] at (marg |- text.base) {$#1$};%
  }%
}

% --- Note number placed 1cm from page edge (left margin) ---
\newcommand{\note}[1]{%
  \tikz[remember picture,overlay,baseline=(text.base)]{%
    \node (text) at (0,0) {};%
    \coordinate (marg) at ($(current page.west)+(\lnotemargin,0)$);%
    \node[
      anchor=base west,
      font=\small\bfseries,
      fill=yellow!30,
      draw=black,
      circle,
      minimum width=18pt,
      minimum height=18pt,
      text width=18pt,   % force fixed width
      align=center,      % center text inside
      inner sep=0pt      % prevent expansion
    ] at (marg |- text.base) {#1};%
  }%
}




% 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})}

\SetEnumitemKey{tight}{
    leftmargin=*,
    itemsep=0pt,
    topsep=0pt,
    parsep=0pt,
    partopsep=0pt,
    before=\vspace{-2pt},   % reduce space before
    after=\vspace{-2pt}     % reduce space after
}

\newcommand{\VMargin}[1]{%
  \begin{tikzpicture}[remember picture,overlay]
    \draw[line width=1pt]
      ([xshift=#1]current page.north west) --
      ([xshift=#1]current page.south west);
  \end{tikzpicture}%
}

\newcommand{\VMarginRight}[1]{%
  \begin{tikzpicture}[remember picture,overlay]
    \draw[line width=0.6pt]
      ([xshift=-#1]current page.north east) --
      ([xshift=-#1]current page.south east);
  \end{tikzpicture}%
}



% 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]{%
\par\vspace{0pt}\noindent\leavevmode
\begin{tikzpicture}[baseline=(text.base)]
    \node[] (text) at (0,0) {\textbf{#1}};
    \fill[black] ([xshift=0.1cm, yshift=-0.1cm]text.south west)
                 rectangle ([xshift=0.1cm, yshift=-0.1cm]text.north east);
    \draw[fill=white] (text.south west) rectangle (text.north east);
    \node[] at (text) {\textbf{#1}};
\end{tikzpicture}\\[0.2cm]
}

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

% --- Header Style 9 (fr)  ---
\newcommand{\printheadnine}{%
  \arrayrulecolor{lightgray}
  \begin{tabularx}{\textwidth}{
      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}
}

\fancyhf{}
\renewcommand{\headrulewidth}{0pt}
\renewcommand{\footrulewidth}{0pt}
\setlength{\headheight}{47pt}
\setlength{\headsep}{0pt}
\fancyhead[C]{%
  \printheadnine
}%
\pagestyle{fancy}




\begin{document}




\VMargin{1.85cm}
\vspace*{-0.75cm}
% Exercise 1 (originally 2)
\printexo{1}{: ( 5 points)}{
\vspace*{-0.5cm}
\begin{enumerate}
  \item \note{1} Déterminer l’abscisse curviligne principale du point ~$A\left(\frac{2026\pi}{6}\right)$~\\
  \item \note{3} Placer les point ~$A$~, ~$B\left(-\frac{\pi}{4}\right)$~ et le point ~$C$~ tel que
    ~$\left(\overline{\overrightarrow{OB},\overrightarrow{OC}}\right)\equiv \frac{-\pi}{2} \,[2\pi]$~
    \item \note{1} Déterminer l'abscisse curviligne principale du point ~$C$~
\end{enumerate}
}

% Exercise 2 (originally 3)
\printexo{2}{: ( 5.5 points)}{
\vspace*{-0.5cm}
\begin{enumerate}
  \item \note{4} Simplifier les expressions suivantes.\\
        ~\(A = 2\sin(x+5\pi) - 3\cos(4\pi-x) + \sin\left(\frac{3\pi}{2}+x\right),\)~\\
        ~\(B = \cos\left(\frac{\pi}{7}\right) + \cos\left(\frac{2\pi}{7}\right) + \cos\left(\frac{5\pi}{7}\right) + \cos\left(\frac{6\pi}{7}\right).\)~
      \item \note{1.5} Soit \(x \in [-\pi;0]\) \quad tel que \quad  \(\cos x = \frac{2}{3}\). Calculer \(\tan x\).
\end{enumerate}
}

% Exercise 3 (originally 5)
\printexo{3}{: ( 10.5 points)}{
Soit \(x\) un nombre réel et \(I = ]-\pi;\pi[\). On pose :
\[f(x) = 2\sqrt{2}\sin x \cdot \cos x - \sqrt{6}\sin x + 2\cos x - \sqrt{3}.\]
\begin{enumerate}[label=\arabic*.]
    \item
        \begin{enumerate}[label=\alph*.]
            \item \note{1} Vérifier que \(f(x) = (\sqrt{2}\sin x + 1)(2\cos x - \sqrt{3})\).
            \item \note{1.5} Calculer : \(f(0),\quad f\left(-\frac{\pi}{4}\right)\quad\text{et}\quad f\left(\frac{\pi}{6}\right)\).
        \end{enumerate}
    \item
        \begin{enumerate}[label=\alph*.]
            \item \note{3} Résoudre dans \(I\) les équations :
                ~\(\sqrt{2}\sin x + 1 = 0 \quad\text{et}\quad 2\cos x - \sqrt{3} = 0.\)~
            \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 :
                ~\(\sqrt{2}\sin x + 1 > 0 \quad\text{et}\quad 2\cos x - \sqrt{3} < 0.\)~
            \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 \(f(x) \le 0\).
        \end{enumerate}
\end{enumerate}
}






% Bottom message
\begin{center}
  \normalsize{%
    \vskip 3pt \hrule height 3pt \vskip 5pt
    \RL{\arabicfont
    ﴿وَكَذَٰلِكَ مَآ أَرْسَلْنَا مِن قَبْلِكَ فِى قَرْيَةٍ مِّن نَّذِيرٍ إِلَّا قَالَ مُتْرَفُوهَآ إِنَّا وَجَدْنَآ ءَابَآءَنَا عَلَىٰٓ أُمَّةٍ وَإِنَّا عَلَىٰٓ ءَاثَـٰرِهِم مُّقْتَدُونَ (23)•  قَـٰلَ أَوَلَوْ جِئْتُكُم بِأَهْدَىٰ مِمَّا وَجَدتُّمْ عَلَيْهِ ءَابَآءَكُمْ ۖ قَالُوٓا۟ إِنَّا بِمَآ أُرْسِلْتُم بِهِۦ كَـٰفِرُونَ (24)• ﴾ \\(الزخرف الآيات 23-24)
    }%
  }%
\end{center}

\end{document}