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Prove that: cot2x + tanx = cosec2x

Consider,

c o t (2 x) + \tan (x) = \frac{\cos (2 x)}{\sin (2 x)} + \tan (x) = \frac{1 - 2 \sin^{2} (x)}{2 \sin (x) \cos (x)} + \tan (x) = \frac{1}{2 \sin (x) \cos (x)} - \frac{2 \sin^{2} (x)}{2 \sin (x) \cos (x)} + \tan (x) = \cos e c (2 x) - \frac{\sin (x)}{\cos (x)} + \tan (x) = \cos e c (2 x) - \tan (x) + \tan (x) = \cos e c (2 x)

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