[Tex/LaTex] Fraction within another fraction

Question

Im using the code as shown below to write a step by step for a question but when i have a fraction in another fraction it becomes small and hard to read. i wish to make the faction inside the same size as the other and clear but not too crowded.

\begin{align*}
    \frac{\sin(a+b)}{\cos(a+b)}&=\frac{\sin a \cos b + \cos a \sin b}{\cos a \cos b - \sin a \sin b}
    \\
    \tan(a+b)&=\frac{\sin a \cos b + \cos a \sin b}{\cos a \cos b - \sin a \sin b}
    \\
    &=\frac{\frac{\sin a \cos b}{\cos a \cos b} + \frac{\cos a \sin b}{\cos a \cos b}}{\frac{\cos a \cos b}{\cos a \cos b} - \frac{\sin a \sin b}{\cos a \cos b}}
    \\
    &=\frac{\frac{\sin a}{\cos a} + \frac{\sin b}{\cos b}}{1 - \frac{\sin a \sin b}{\cos a \cos b}}
    \\
    &=\frac{\tan a +\tan b }{1 - \tan a \tan b}
\end{align*}

Answer 1

You can use \cfrac for nested fractions. However this makes the ‘upper’ denominators too close from the main fraction line, so one can compensate adding a phantom letter with descenders. No compensation required for the ‘lower’ numerators if you use \cfrac (not \dfrac).

Another possibility would use the \mfrac(medium-sized fraction – 80 % of \displaystyle) command from nccmath, so the smaller fractions are still readable. Here is an example of both methods:

\documentclass{article}
\usepackage{amsmath, nccmath}

\begin{document}

    \begin{align*}
        \frac{\sin(a+b)}{\cos(a+b)}&=\frac{\sin a \cos b + \cos a \sin b}{\cos a \cos b - \sin a \sin b}
        \\
        \tan(a+b)&=\frac{\sin a \cos b + \cos a \sin b}{\cos a \cos b - \sin a \sin b}
        \\[0.5ex]
        &=\frac{\cfrac{\sin a \cos b}{\cos a \cos b} + \cfrac{\cos a \sin b}{\cos a \cos b\vphantom{g}}}{\cfrac{\cos a \cos b}{\cos a \cos b} - \cfrac{\sin a \sin b}{\cos a \cos b}}
        \\[0.5ex]
        &=\frac{\cfrac{\sin a}{\cos a} + \cfrac{\sin b}{\cos b \vphantom{g}}}{1 - \cfrac{\sin a \sin b}{\cos a \cos b}}
        \\[0.5ex]
        &=\frac{\tan a +\tan b }{1 - \tan a \tan b}
    \end{align*}\medskip

    \begin{align*}
        \frac{\sin(a+b)}{\cos(a+b)}&=\frac{\sin a \cos b + \cos a \sin b}{\cos a \cos b - \sin a \sin b}
        \\
        \tan(a+b)&=\frac{\sin a \cos b + \cos a \sin b}{\cos a \cos b - \sin a \sin b}
        \\[0.5ex]
        &=\frac{\mfrac{\sin a \cos b}{\cos a \cos b} + \mfrac{\cos a \sin b}{\cos a \cos b\vphantom{g}}}{\mfrac{\cos a \cos b}{\cos a \cos b} - \mfrac{\sin a \sin b}{\cos a \cos b}}
        \\[0.5ex]
        &=\frac{\mfrac{\sin a}{\cos a} + \mfrac{\sin b}{\cos b\vphantom{g}}}{1 - \mfrac{\sin a \sin b}{\cos a \cos b}}
        \\[0.5ex]
        &=\frac{\tan a +\tan b }{1 - \tan a \tan b}
    \end{align*}

\end{document}