What is $cot θ + {tan}^{3} θ$ $cot theta + tan ^3 theta$ in terms of $sin θ$ $sintheta$ ?

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What is $cot θ + {tan}^{3} θ$ $cot theta + tan ^3 theta$ in terms of $sin θ$ $sintheta$ ?

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Answer 1 · 2016-03-05T06:08:06

$cot θ + {tan}^{3} θ$ $cottheta+tan^3theta$
$= \frac{cos θ}{sin θ} + \frac{{sin}^{3} θ}{{cos}^{3} θ}$ $=costheta/sintheta+sin^3theta/cos^3theta$
$= \frac{{cos}^{4} θ + {sin}^{4} θ}{sin θ \cdot {cos}^{3} θ}$ $=(cos^4theta+sin^4theta)/(sintheta*cos^3theta$
$= \frac{{({cos}^{2} θ + {sin}^{2} θ)}^{2} - 2 {sin}^{2} θ {cos}^{2} θ}{sin θ {(1 - {sin}^{2} θ)}^{\frac{3}{2}}}$ $=((cos^2theta+sin^2theta)^2-2sin^2thetacos^2theta)/(sintheta(1-sin^2theta)^(3/2)$
$= \frac{1 - 2 {sin}^{2} θ (1 - {sin}^{2} θ)}{sin θ {(1 - {sin}^{2} θ)}^{\frac{3}{2}}}$ $=(1-2sin^2theta(1-sin^2theta))/(sintheta(1-sin^2theta)^(3/2)$

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What is $cot θ + {tan}^{3} θ$ $cot theta + tan ^3 theta$ in terms of $sin θ$ $sintheta$ ?

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