User:Ixlusion

$(1+\sec\theta)(\csc\theta-\cot\theta)\,$

$= \csc\theta - \cot\theta + \sec\theta\csc\theta - \cot\theta\sec\theta\,$

$= \frac{1}{\sin\theta} - \frac{\cos\theta}{\sin\theta} + \frac{1}{\sin\theta\cos\theta} - (\frac{\cos\theta}{\sin\theta} * \frac{1}{\cos\theta}) \,$

$= \frac{1}{\sin\theta\cos\theta} - \frac{\cos\theta}{\sin\theta} \,$

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

$= \frac{\sin^2\theta}{\sin\theta\cos\theta} \,$

$= \frac{\sin\theta}{\cos\theta} \,$

$= \tan\theta \,$