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Prove that (cosec A – sin A) (sec A – cos A) = 1/tan A + cot A

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Prove that (cosec A – sin A) (sec A – cos A) = \(\frac{1}{tan\,A+cot\,A}\)

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L.H.S. = (cosec A – sin A) (sec A – cos A)

Now

From (1) and (2), we get 

L.H.S. = R.H.S. 

∴ (cosec A – sin A) (sec A – cos A) = \(\frac{1}{tan\,A+cot\,A}\)

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