# How do you prove that costheta/(1-sintheta) + costheta/(1+sintheta) = 2 /costheta?

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#### Explanation

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#### Explanation:

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Bdub Share
Mar 8, 2018

See Below

#### Explanation:

$L H S : \cos \frac{\theta}{1 - \sin \theta} + \cos \frac{\theta}{1 + \sin \theta}$

$= \frac{\cos \theta \left(1 + \sin \theta\right) + \cos \theta \left(1 - \sin \theta\right)}{\left(1 - \sin \theta\right) \left(1 + \sin \theta\right)}$->common denominator

$= \frac{\cos \theta + \sin \theta \cos \theta + \cos \theta - \sin \theta \cos \theta}{1 - {\sin}^{2} \theta}$

$= \frac{\cos \theta + \cancel{\sin \theta \cos \theta} + \cos \theta - \cancel{\sin \theta \cos \theta}}{1 - {\sin}^{2} \theta}$

$= \frac{2 \cos \theta}{\cos} ^ 2 \theta$->use the property ${\sin}^{2} \theta + {\cos}^{2} \theta = 1$

$= \frac{2 \cancel{\cos} \theta}{\cos} ^ \cancel{2} \theta$

$= \frac{2}{\cos} \theta$

$= R H S$

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