How do you simplify ${cot}^{2} x - {cot}^{2} x {cos}^{2} x$ $cot^2x - cot^2x cos^2x$ ?

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Answer 1 · 2018-05-25T18:09:21

${cos}^{2} x$ $cos^2 x$

Given: ${cot}^{2} x - {cot}^{2} x {cos}^{2} x$ $cot^2x - cot^2 x cos^2x$

Factor: ${cot}^{2} x (1 - {cos}^{2} x)$ $cot^2x (1 - cos^2x)$

Use the Pythagorean trigonometric identity: ${sin}^{2} x + {cos}^{2} x = 1$ $sin^2x + cos^2x = 1$

Rearrange the identity: ${sin}^{2} x = 1 - {cos}^{2} x$ $sin^2x = 1 - cos^2x$

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

Use the identity: $cot x = \frac{cos x}{sin x}$ $cot x= (cos x)/(sin x)$

Realize that ${cot}^{2} x = {(cot x)}^{2}$ $cot^2x = (cot x)^2$

$cot^2x (1 - cos^2x) = (cos^2 x)/cancel(sin^2 x) cancel(sin^2x) = cos^2x$

How do you simplify cot^2x - cot^2x cos^2xcot2x−cot2xcos2xcot^2x - cot^2x cos^2x?