\documentclass{standalone}
\standaloneconfig{margin=1cm}
\usepackage{fontspec}
\usepackage{tikz,tkz-tab}
\usepackage{xcolor}
\usepackage{amsmath, amsfonts, amssymb, amsthm}
\usetikzlibrary{calc}
\usetikzlibrary{shapes,decorations.text, intersections}
\definecolor{RoyalBlue}{HTML}{4169E1} % Royal Blue
\definecolor{ocre}{RGB}{243,102,25} % orange color
\definecolor{DarkGreen}{HTML}{006400} % Dark Green
\everymath{\displaystyle}
\begin{document}
\begin{tikzpicture}
\node at (0,0) {
\begin{tikzpicture}
\tkzTabInit[lgt=4, espcl=2.5] %
{$x$ /1.75, $1+\tan x$ /1, $\sin 2x$ /1, $\frac{1+\tan x}{\sin 2x}$/1.75}
{$-\pi$,$\frac{-\pi}{2}$,$\frac{-\pi}{4}$,$0$,$\frac{\pi}{2}$,$\frac{3\pi}{4}$,$\pi$}
\tkzTabLine{ , +, d, -, z, +, t, +, d, -, z, +}
\tkzTabLine{z, -, t, -, t, -, z, +, t, +, t, +,z}
\tkzTabLine{d, -, d, +, z, -, z, +, d, -, z, +,d}
\end{tikzpicture}
};
\node[align=left,text width=10cm] at (2.5,7) {
~$ x\in]-\pi,\pi]\quad \frac{1+\tan x}{\sin(2x)}\ge0$
};
\node[align=left,text width=10cm] at (2.5,5) {
~$ S=\left]\frac{-\pi}{2},\frac{-\pi}{4}\right]\cup\left[0,\frac{\pi}{2}\right]\cup\left[\frac{3\pi}{4},\pi\right[$
};
\node at (7.5,5.5) {
\begin{tikzpicture}
\coordinate (A) at (0,0);
\draw[red!50] (A) circle (1.9cm);
% Draw the inner circle
\draw[red!50] (A) circle (1.4cm);
% Draw the curved line
\draw[red!50, decorate, decoration={text along path,
text={|\fontspec{DejaVu Sans}\color{red!75}\bfseries|★MOSAID RADOUAN★},
text align={align=center}, raise=-3pt}] (A) ++ (180:1.6cm) arc (180:0:1.6cm);
\draw[decorate, decoration={text along path,
text={|\fontspec{DejaVu Sans}\color{red!75}\bfseries|∞★~mosaid.xyz~★∞ },
text align={align=center}, raise=-6.5pt}] (A) ++ (180:1.53cm) arc (-180:0:1.53cm);
\node[red!75,font=\fontsize{48}{48}\fontspec{DejaVu Sans}\bfseries\selectfont] at (A) {✷};
\end{tikzpicture}
};
\node at (-6.5,5.5) {
\begin{tikzpicture}
\def\radius{1.5} %
\coordinate (O) at (0,0);
\coordinate (I) at (\radius,0);
\coordinate (M) at (-45:\radius);
\coordinate (M') at (135:\radius);
\node[above left ] at (O) {$O$};
\node[above right] at (I) {$I$};
\fill (O) circle (1.5pt);
\draw (O) circle (\radius);
\draw[] (-1.2*\radius,0) -- (1.2*\radius,0);
\draw[] (0,-1.2*\radius) -- (0,1.2*\radius);
\draw[DarkGreen, line width=0.3mm, name path = tangente] (\radius,-2) -- (\radius,2.5) ;
\foreach \x in {-3,-2.9 , ...,0.5} {
\draw[RoyalBlue, thick] (\radius-0.1,\x+\radius) -- ++(0.2,0); %
}
\draw[thick] (\radius-0.1,\radius) -- ++(0.2,0) node[right] {$1$}; %
\path [name path=OM] (O) -- ($(O)!3.5!(M)$);
\path [name intersections={of=OM and tangente, by=T}];
\fill (M) circle (1.5pt);
\fill (M') circle (1.5pt);
\fill (T) circle (1.5pt);
\draw[RoyalBlue, line width=0.5mm] ($(M)!1.2!(M')$) -- (M);
\draw[RoyalBlue, line width=0.5mm, dashed] (M') -- ($(M')!1.2!(T)$);
\node[above, font=\small, yshift=0.1cm] at (M) {$M$};
\node[below, font=\tiny] at (M) {$\frac{-\pi}{4}$};
\node[below, font=\small,yshift=-0.2cm] at (M') {$M'$};
\node[above, font=\tiny] at (M') {$\frac{3\pi}{4}$};
\draw[red, line width=0.7mm] (M) arc(-45:90:\radius);
\draw[red, line width=0.7mm] (M') arc(135:270:\radius);
\node[above, font=\small] at (90:1.2*\radius) {$\frac{\pi}{2}$};
\node[above left, font=\small] at (90:\radius) {$J$};
\node[below left, font=\small] at (-90:\radius) {$J'$};
\node[below, font=\small] at (-90:1.2*\radius) {$\frac{-\pi}{2}$};
\node[below left, font=\small] at (-\radius,0) {$-\pi$};
\node[above left, font=\small] at (-\radius,0) {$\pi$};
\node[right, font=\tiny] at (T) {$-1$};
\end{tikzpicture}\\
};
\end{tikzpicture}
\end{document}
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