Source TeX:

\begin{array}{rll}\tan^2(y)+1&=\sec^2(y)&\\x^2+1&=\sec^2(y)&\small\text{; car }\tan(y)=x\\\sqrt{x^2+1}&=+\sec(y)&\small\text{ puisque }y\in\left]-\frac{\pi}{2},\frac{\pi}{2}\right[,\\[-0.5em]&&\small\text{ alors }\sec{y} > 0\\\sqrt{x^2+1}&=\dfrac{1}{\cos(y)}&\\\cos(y)&=\dfrac{1}{\sqrt{x^2+1}}&\end{array}