How do you prove $\frac{csc θ}{sin θ} = {csc}^{2} θ$ $csctheta/sintheta=csc^2theta$ ?

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How do you prove $\frac{csc θ}{sin θ} = {csc}^{2} θ$ $csctheta/sintheta=csc^2theta$ ?

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Answer 1 · 2016-10-07T20:08:34

Easy! Just remember that $\frac{1}{sin θ} = csc θ$ $1/ sin theta = csc theta$ and you will find that $\frac{csc θ}{sin θ} = {csc}^{2} θ$ $csc theta / sin theta = csc^2 theta$

Explanation:

To prove that $\frac{csc θ}{sin θ} = {csc}^{2} θ$ $csc theta / sin theta = csc^2 theta$ , we have to remember that $csc θ = \frac{1}{sin θ}$ $csc theta = 1/ sin theta$

Proof: $\frac{csc θ}{sin θ} = {csc}^{2} θ$ $csc theta / sin theta = csc^2 theta$

$\frac{\frac{1}{sin θ}}{sin θ} = {csc}^{2} θ$ $(1/ sin theta) / sin theta = csc^2 theta$

$\frac{1}{sin θ} \cdot \frac{1}{sin θ} = {csc}^{2} θ$ $1/ sin theta * 1/ sin theta = csc^2 theta$

$\frac{1}{{sin}^{2} θ} = {csc}^{2} θ$ $1/ sin^2 theta = csc^2 theta$
So, ${csc}^{2} θ = {csc}^{2}$ $csc^2 theta = csc^2$

There you go :)

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How do you prove $\frac{csc θ}{sin θ} = {csc}^{2} θ$ $csctheta/sintheta=csc^2theta$ ?

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How do you prove $\frac{csc θ}{sin θ} = {csc}^{2} θ$ $csctheta/sintheta=csc^2theta$ ?