Question

Cosec X - sin x= cos x cotx
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Answer 1

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Step-by-step explanation:

`cosec \: x - sin \: x = cos \: x \: cot \: x \\ \\ L.H.S\\= cosec \: x - sin \: x \\ = (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)\\ \\ = (cos \: x * cos \: x)/( \sin \: x) \\ \\ = \cos \: x * (\cos \: x)/( \sin \: x) \\ \\ = \cos x \: \cot x \\ = R.H.S\\ Thus \: proved \\`