Question #011db

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Question #011db

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Answer 1 · 2017-04-27T01:20:12

Proved.

Explanation:

Given: $\frac{{sec}^{2} (x)}{{sec}^{2} (x) - 1} = {csc}^{2} (x)$ $sec^2(x)/(sec^2(x)-1) =csc^2(x)$

Because $cos (x) sec (x) = 1$ $cos(x)sec(x) = 1$ , we shall multiply the the fraction by 1 in the form $\frac{{cos}^{2} (x)}{{cos}^{2} (x)}$ $cos^2(x)/cos^2(x)$ :

$\frac{{cos}^{2} (x)}{{cos}^{2} (x)} \frac{{sec}^{2} (x)}{{sec}^{2} (x) - 1} = {csc}^{2} (x)$ $cos^2(x)/cos^2(x)sec^2(x)/(sec^2(x)-1) =csc^2(x)$

This simplifies to the following:

$\frac{1}{1 - {cos}^{2} (x)} = {csc}^{2} (x)$ $1/(1-cos^2(x)) =csc^2(x)$

We know that $1 - {cos}^{2} (x) = {sin}^{2} (x)$ $1 - cos^2(x) = sin^2(x)$ :

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

We know that ${csc}^{2} (x) = \frac{1}{{sin}^{2} (x)}$ $csc^2(x) = 1/sin^2(x)$

${csc}^{2} (x) = {csc}^{2} (x)$ $csc^2(x) =csc^2(x)$

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Question #011db

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