Solve tan 2x - cot x = 0 for the interval [0, 2pi)

Use the following identities: cot x = 1/tanx. and tan 2x = (2tanx)/(1-tan

^{2}x)The equation then becomes (2tanx)/(1-tan

^{2}x) - 1/(tanx) = 0Add 1/(tanx) to each side: (2tanx)/(1-tan

^{2}x) = 1/(tanx).Multiply each side by tanx*(1-tan

^{2}x): 2tan^{2}x = 1-tan^{2}x.Combine terms: 3tan

^{2}x = 1, divide by 3: tan^{2}x = 3, so tanx = √3 and tanx = -√3.so x = π/3 in each of the 4 quadrants.

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