How do you simplify $\frac{{csc}^{2} x - {cot}^{2} x}{sec x}$ $(csc^2 x - cot^2 x)/secx$ ?

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How do you simplify $\frac{{csc}^{2} x - {cot}^{2} x}{sec x}$ $(csc^2 x - cot^2 x)/secx$ ?

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Answer 1 · 2018-06-18T10:49:44

$cos x$ $cosx$

Explanation:

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

$= (\frac{1}{{sin}^{2} x} - \frac{{cos}^{2} x}{{sin}^{2} x}) \cdot cos x$ $=(1/sin^2x-cos^2x/sin^2x)*cosx$

$= \frac{1 - {cos}^{2} x}{{sin}^{2} x} \cdot cos x$ $=(1-cos^2x)/sin^2x*cosx$

$=cancel(sin^2x)/cancel(sin^2x)*cosx$

$=cosx$

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How do you simplify $\frac{{csc}^{2} x - {cot}^{2} x}{sec x}$ $(csc^2 x - cot^2 x)/secx$ ?

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