Question

Cosec X - sin x= cos x cotx​

Answer 1

Answer:

See Explanation

Explanation:

$cosec \: x - sin \: x = cos \: x \: cot \: x \\ \\ L.H.S\\= cosec \: x - sin \: x \\ = \frac{1}{sin \: x} - sin \: x \\ \\ = \frac{1 - { \sin}^{2}x }{sin \: x} \\ \\ = \frac{ { \cos}^{2}x }{sin \: x} ...( \because \: 1 - { \sin}^{2} \theta = { \cos}^{2} \theta)\\ \\ = \frac{cos \: x \times cos \: x}{ \sin \: x} \\ \\ = \cos \: x \times \frac{\cos \: x}{ \sin \: x} \\ \\ = \cos x \: \cot x \\ = R.H.S\\ Thus \: proved$