csc(-x)/1+tan^2x) = ?

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03-08-2017
Mathematics

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csc(-x)/1+tan^2x) = ?

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jdoe0001 jdoe0001 · Answer 1 · 2017-08-04T01:53:48+02:00

[tex]\bf 1+tan^2(\theta)=sec^2(\theta)\qquad \qquad sin(-\theta )=-sin(\theta ) \\\\\\ cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}\qquad \qquad csc(\theta)=\cfrac{1}{sin(\theta)} \qquad \qquad % secant sec(\theta)=\cfrac{1}{cos(\theta)}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{csc(-x)}{1+tan^2(x)} \implies \cfrac{csc(-x)}{sec^2(x)}\implies \cfrac{\frac{1}{sin(-x)}}{\frac{1^2}{cos^2(x)}} \\\\\\ \cfrac{1}{-sin(x)}\cdot \cfrac{cos^2(x)}{1}\implies -\cfrac{cos^2(x)}{sin(x)}\implies cos(x)\cfrac{cos(x)}{sin(x)} \\\\\\ \boxed{cos(x)cot(x)}[/tex]