[tex]\bf sin^2(\theta)+cos^2(\theta)=1\to
\begin{cases}
cos^2(\theta)=1-sin^2(\theta)\\
sin^2(\theta)=1-cos^2(\theta)
\end{cases} \\\\
-------------------------------\\\\
\stackrel{\textit{difference of squares}}{\cfrac{[1-cos(\theta )][1+cos(\theta )]}{[1-sin(\theta )][1+sin(\theta )]}}\implies \cfrac{1^2-cos^2(\theta )}{1^2-sin^2(\theta )}\implies \cfrac{1-cos^2(\theta )}{1-sin^2(\theta )}
\\\\\\
\cfrac{sin^2(\theta )}{cos^2(\theta )}\implies tan^2(\theta )[/tex]
