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Prove the following: (1/ tan 3A-tan A) - (1/ cot 3A- cot A) = cot 2A

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Prove the following:

\(\frac{1}{tan\, 3A-tan\,A}-\frac{1}{cot\,3A-cot\,A} = cot\, 2A\)

(1/ tan 3A-tan A) - (1/ cot 3A- cot A) = cot 2A

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L.H.S. = \(\frac{1}{tan\, 3A-tan\,A}-\frac{1}{cot\,3A-cot\,A}\)

           = \(\frac{1}{tan\, 3A-tan\,A}-\frac{1}{\frac{1}{tan\,3A}-\frac{1}{tan\,A}}\)

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