What is $\frac{{cot}^{4} θ}{1 - {cos}^{4} θ}$ $cot^4theta/(1-cos^4theta)$ in terms of non-exponential trigonometric functions?

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What is $\frac{{cot}^{4} θ}{1 - {cos}^{4} θ}$ $cot^4theta/(1-cos^4theta)$ in terms of non-exponential trigonometric functions?

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Answer 1 · 2018-03-14T02:22:21

$\frac{cot θ \cdot cot θ}{sin θ \cdot sin θ \cdot sin θ \cdot sin θ}$ $(cottheta*cottheta)/(sintheta*sintheta*sintheta*sintheta)$

Explanation:

This answer is incorrect!

${cot}^{4} θ = \frac{{cos}^{4} θ}{{sin}^{4} θ}$ $cot^4 theta = cos^4 theta/sin^4 theta$

$1 - {cos}^{2} θ = {sin}^{2} θ$ $1-cos^2 theta = sin^2 theta$

Here is where the mistake was made:
$\frac{{cot}^{4} θ}{1 - {cos}^{4} θ} = \frac{\frac{{cos}^{4} θ}{{sin}^{4} θ}}{{sin}^{2} θ \cdot {cos}^{2} θ}$ $cot^4 theta / (1-cos^4 theta) = (cos^4 theta/sin^4 theta)/(sin^2 theta*cos^2 theta$

$\frac{\frac{{cos}^{4} θ}{{sin}^{4} θ}}{{sin}^{2} θ \cdot {cos}^{2} θ} = \frac{\frac{{cos}^{2} θ}{{sin}^{4} θ}}{{sin}^{2} θ}$ $(cos^4 theta/sin^4 theta)/(sin^2 theta*cos^2 theta) = (cos^2 theta/sin^4 theta)/(sin^2 theta)$

$\frac{\frac{{cos}^{2} θ}{{sin}^{4} θ}}{\frac{{sin}^{2} θ}{1}}$ $(cos^2 theta/sin^4 theta)/(sin^2 theta/1)$ or $\frac{{cos}^{2} θ}{{sin}^{4} θ} \cdot \frac{1}{{sin}^{2} θ}$ $cos^2 theta/sin^4 theta*1/sin^2 theta$

Multiply across

$\frac{{cos}^{2} θ}{{sin}^{6} θ}$ $cos^2 theta/sin^6 theta$ = $\frac{{cot}^{2} θ}{{sin}^{4} θ}$ $cot^2 theta/sin^4 theta$

Expand to get rid of the exponents

$\frac{cot θ \cdot cot θ}{sin θ \cdot sin θ \cdot sin θ \cdot sin θ}$ $(cottheta*cottheta)/(sintheta*sintheta*sintheta*sintheta)$

I hope this is the form you were looking for!

Answer 2 · 2018-03-14T02:57:45

$\frac{\frac{cos x}{sin x} \cdot \frac{cos x}{sin x} \cdot \frac{cos x}{sin x} \cdot \frac{cos x}{sin x}}{(sin x \cdot sin x + sin x \cdot sin x \cdot cos x \cdot cos x)}$ $(cosx/sinx*cosx/sinx*cosx/sinx*cosx/sinx)/((sinx*sinx+sinx*sinx*cosx*cosx))$

Explanation:

$\frac{{cot}^{4} x}{1 - {cos}^{4} x} =$ $cot^4x/(1-cos^4x)=$
$\frac{{cot}^{4} x}{(1 - {cos}^{2} x) (1 + {cos}^{2} x)} =$ $cot^4x/((1-cos^2x)(1+cos^2x))=$
$\frac{{cot}^{4} x}{({sin}^{2} x) (1 + {cos}^{2} x)} =$ $cot^4x/((sin^2x)(1+cos^2x))=$

$\frac{\frac{cos x}{sin x} \cdot \frac{cos x}{sin x} \cdot \frac{cos x}{sin x} \cdot \frac{cos x}{sin x}}{(sin x \cdot sin x + sin x \cdot sin x \cdot cos x \cdot cos x)}$ $(cosx/sinx*cosx/sinx*cosx/sinx*cosx/sinx)/((sinx*sinx+sinx*sinx*cosx*cosx))$

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What is $\frac{{cot}^{4} θ}{1 - {cos}^{4} θ}$ $cot^4theta/(1-cos^4theta)$ in terms of non-exponential trigonometric functions?

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What is cot^4theta/(1-cos^4theta)cot4θ1−cos4θcot^4theta/(1-cos^4theta) in terms of non-exponential trigonometric functions?

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What is $\frac{{cot}^{4} θ}{1 - {cos}^{4} θ}$ $cot^4theta/(1-cos^4theta)$ in terms of non-exponential trigonometric functions?