wezergoat420l2k

2022-12-31

How to simplify $\frac{{\mathrm{cos}}^{2}x}{1-{\mathrm{cos}}^{2}x}$?

Mikayla Cox

Expert

Using the identity can help to make this simpler.
${\mathrm{sin}}^{2}x+{\mathrm{cos}}^{2}x=1$
From this we can see that
${\mathrm{sin}}^{2}x=1-{\mathrm{cos}}^{2}x$
Hence we have
$\frac{{\mathrm{cos}}^{2}x}{1-{\mathrm{cos}}^{2}x}=\frac{{\mathrm{cos}}^{2}x}{{\mathrm{sin}}^{2}x}={\mathrm{cot}}^{2}x$

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