# Find the value of cos theta/1-sin theta + cos theta/1+sin theta=4?

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Bdub Share
Apr 17, 2016

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#### Explanation:

$\cos \frac{\theta}{1 - \sin \theta} + \cos \frac{\theta}{1 + \sin \theta} = 4$

$\frac{\cos \theta \left(1 + \sin \theta\right) + \cos \theta \left(1 - \sin \theta\right)}{\left(1 - \sin \theta\right) \left(1 + \sin \theta\right)} = 4$

$\frac{\cos \theta + \sin \theta \cos \theta + \cos \theta - \sin \theta \cos \theta}{1 - {\sin}^{2} \theta} = 4$

$\frac{2 \cos \theta}{\cos} ^ 2 \theta = 4$

$\frac{2}{\cos} \theta = 4$

$2 = 4 \cos \theta$

$\frac{1}{2} = \cos \theta$

$\theta = {\cos}^{-} 1 \left(\frac{1}{2}\right)$

$\theta = \pm 60 + {360}^{\circ} n$

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