User:Ixlusion


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

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

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

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

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

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

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

$$= \tan\theta \, $$