# Solve cot^2 theta -cos^2theta

Question
Solve $$\displaystyle{{\cot}^{{2}}\theta}-{{\cos}^{{2}}\theta}$$

2021-02-06
$$\displaystyle{\left(\frac{{{\cos}^{{2}}\theta}}{{{\sin}^{{2}}\theta}}\right)}-{{\cos}^{{2}}\theta}={{\cos}^{{2}}\theta}{\left(\frac{{1}}{{{\sin}^{{2}}\theta}}-{1}\right)}=$$
$$\displaystyle{{\cos}^{{2}}\theta}\frac{{{1}-{{\sin}^{{2}}\theta}}}{{{\sin}^{{2}}\theta}}=\frac{{{\cos}^{{2}}\theta}}{{{\sin}^{{2}}\theta}}={{\cot}^{{2}}\theta}{{\cos}^{{2}}\theta}.$$

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