How do you simplify $\frac{cos θ csc θ}{tan θ}$ $(cos theta csc theta)/tantheta$ ?

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How do you simplify $\frac{cos θ csc θ}{tan θ}$ $(cos theta csc theta)/tantheta$ ?

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Answer 1 · 2015-07-28T13:02:23

Use the following:
$csc θ = \frac{1}{sin θ}$ $csctheta=1/sintheta$

$tan θ = \frac{sin θ}{cos θ}$ $tantheta=sintheta/costheta$

Explanation:

$\frac{cos θ csc θ}{tan θ} = \frac{(cos θ) \cdot \frac{1}{sin θ}}{\frac{sin θ}{cos θ}}$ $(cos theta csc theta)/tantheta=((costheta)*1/sintheta)/(sintheta/costheta)$

$= \frac{cos θ}{sin θ} \cdot (\frac{cos θ}{sin θ}) = \frac{{(cos θ)}^{2}}{{(sin θ)}^{2}} = {(\frac{cos θ}{sin θ})}^{2} = {(cot θ)}^{2} = {cot}^{2} (θ)$ $=costheta/sintheta*(costheta/sintheta)=(costheta)^2/(sintheta)^2=(costheta/sintheta)^2=(cottheta)^2=color(blue)(cot^2(theta))$

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How do you simplify $\frac{cos θ csc θ}{tan θ}$ $(cos theta csc theta)/tantheta$ ?

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