Question

tan theta - cot theta/sin theta cos theta=sec2 theta-cosec2 theta.

Answer 1

Answer:

refer to the above attachment for the proof

Answer 2

$\frac{tan \theta - cot \theta}{sin \theta cos \theta} \\ \\ = \frac{ \frac{sin \theta}{cos \theta} - \frac{cos \theta}{sin \theta} }{sin \theta - cos \theta} \\ \\ = \frac{ {sin}^{2} \theta - {cos}^{2} \theta }{ {sin}^{2} \theta {cos}^{2} \theta}$

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