Question

cosec theta - cot theta = sin theta upon 1 + cos theta​

Answer 1

$cosec \theta - cot \theta \\ = \frac{1 - cos\theta}{sin \theta} \\ = \frac{1 - cos \theta}{sin \theta} \times \frac{1 + cos \theta}{1 + cos \theta} \\ = \frac{1 - {cos}^{2} \theta }{sin \theta(1 + cos \theta)} \\ = \frac{ {sin}^{2} \theta }{sin \theta(1 + cos \theta)} \\ = \frac{sin \theta}{1 + cos \theta}$