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ahrayia [7]
4 years ago
11

Cosec X - sin x= cos x cotx​

English
1 answer:
madreJ [45]4 years ago
6 0

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 \\

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