Question

sec theta minus cosec theta into 1 + tan theta + cot theta is equal to tan theta into sec theta minus cos theta into cosec theta​

Answer 1

Solution:

$(sec \: \theta - cosec\theta )(1 + tan \: \theta + cot \: \theta) \\ \\ \bigg( \frac{1}{cos \: \theta} - \frac{1}{sin \: \theta} \bigg)\bigg(1 + \frac{sin \: \theta}{cos \: \theta} + \frac{cos \: \theta}{sin \: \theta}\bigg) \\ \\ \bigg( \frac{sin \: \theta - cos \: \theta}{sin \: \theta \: cos \: \theta} \bigg)\bigg( \frac{sin \: \theta \: cos \: \theta + {sin}^{2} \theta + {cos}^{2} \theta}{sin \: \theta \: cos \: \theta} \bigg) \\ \\ \frac{(sin \: \theta - cos \: \theta)({sin \: \theta \: cos \: \theta +1)}}{sin \: \theta \: cos \: \theta} \\ \\ \frac{ {sin}^{2} \theta \: cos \: \theta + sin \: \theta - sin \: \theta {cos}^{2}\theta - cos \: \theta }{sin \: \theta \: cos \: \theta} \\ \\ \frac{ {sin}^{2}\theta \: cos \: \theta - cos \: \theta + sin \: \theta - sin \: \theta {cos}^{2} \theta }{sin \: \theta \: cos \: \theta} \\ \\ \frac{cos \: \theta( {sin}^{2} \theta - 1) + sin \: \theta(1 - {cos}^{2}\theta) }{sin \: \theta \: cos \: \theta} \\ \\ \frac{ - cos \: \theta {cos}^{2}\theta + sin \: \theta {sin}^{2}\theta }{sin \: \theta \: cos \: \theta} \\ \\ \frac{sin \: \theta \: {sin}^{2} \theta}{sin \: \theta \: cos \: \theta} - \frac{cos \: \theta \: {cos}^{2} \theta}{sin \: \theta \: cos \: \theta} \\ \\ \frac{ {sin}^{2} \theta}{cos \: \theta} - \frac{ {cos}^{2} \theta}{sin \:\theta} \\ \\ \frac{sin \: \theta}{cos \: \theta} sin \: \theta - \frac{cos \: \theta}{sin \: \theta} cos \: \theta \\ \\ tan \: \theta \: sin \: \theta - cot \: \theta \: cos \: \theta$

Answer 2

Answer:

ok done hope it help you