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cotA- tanA=2Cot2A

LHS = \cot A - \tan A = \frac{\cos A}{\sin A} - \frac{\sin A}{\cos A} = \frac{\cos^{2} A - \sin^{2} A}{\sin A . \cos A} = \frac{\cos 2 A}{\sin A . \cos A} = \frac{2 \cos 2 A}{2 \sin A . \cos A} = \frac{2 \cos 2 A}{\sin 2 A} = 2 \cot 2 A = RHS

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