How do you simplify $\frac{{cos}^{2} x}{1 - {cos}^{2} x}$ $cos^2x / (1-cos^2x)$ ?

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Answer 1 · 2015-07-26T01:33:19

${cot}^{2} x$ $cot^2x$

One way to simplify this is to use the identity

${sin}^{2} x + {cos}^{2} x = 1$ $sin^2x+cos^2x=1$

From this we can see that

${sin}^{2} x = 1 - {cos}^{2} x$ $sin^2x=1-cos^2x$

Therefore we have

$\frac{{cos}^{2} x}{1 - {cos}^{2} x} = \frac{{cos}^{2} x}{{sin}^{2} x} = {cot}^{2} x$ $cos^2x/(1-cos^2x)=cos^2x/sin^2x=cot^2x$

How do you simplify cos2x1−cos2x cos^2x / (1-cos^2x)?