Simplify ^@ \dfrac{\cos \theta } { 1 + \sin \theta } + \dfrac{ 1 + \sin \theta } { \cos \theta } ^@.


Answer:

^@ 2sec θ ^@

Step by Step Explanation:
  1. ^@ \begin{align} & \dfrac{\cos \theta } { 1 + \sin \theta } + \dfrac{ 1 + \sin \theta } { \cos \theta } \\ = & \dfrac{\cos \theta \cos \theta + (1 + \sin \theta) ( 1 + \sin \theta)} { (1 + \sin \theta) \cos \theta } \\ = & \dfrac{\cos^2 \theta + 1 + \sin^2 \theta + 2 \sin \theta}{ (1 + \sin \theta) \cos \theta } \\ = & \dfrac{2 + 2 \sin \theta} {(1 + \sin \theta) \cos \theta } \\ = & \dfrac{2 (1 + \sin \theta)} {(1 + \sin \theta) \cos \theta } \\ = & 2sec θ \end{align} ^@

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