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cot x +tan x =2 cosec x

$\cot x + \tan x = 2 cosec x \Rightarrow \frac{\cos x}{\sin x} + \frac{\sin x}{\cos x} = \frac{2}{\sin x} \Rightarrow \frac{\cos^{2} x + \sin^{2} x}{\sin x \cos x} = \frac{2}{\sin x} \Rightarrow \frac{1}{\sin x \cos x} = \frac{2}{\sin x} \Rightarrow 2 \sin x \cos x - \sin x = 0 \Rightarrow \sin x (2 \cos x - 1) = 0 \Rightarrow \sin x = 0 or 2 \cos x - 1 = 0 \Rightarrow \sin x = 0 or \cos x = \frac{1}{2} \Rightarrow x = n π or x = 2 n π \pm \frac{π}{3}, n \in Z$

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