Answer
$\dfrac{\cos{\theta}+1}{\cos{\theta}}$
Work Step by Step
Factor each expression:
$\cos^2{\theta}-1 = (\cos{\theta}+1)(\cos{\theta}-1)$
$\cos^2{\theta}-\cos{\theta} = \cos{\theta}(\cos{\theta}-1)$
Thus,
$\dfrac{\cos^2{\theta}-1}{\cos^2{\theta}-\cos{\theta}} =\dfrac{(\cos{\theta}+1)(\cos{\theta}-1)}{\cos{\theta}(\cos{\theta}-1)}$
Cancek the common factors to obtain:
$\dfrac{(\cos{\theta}+1)(\cos{\theta}-1)}{\cos{\theta}(\cos{\theta}-1)} = \boxed{\dfrac{\cos{\theta}+1}{\cos{\theta}}}$
