Solve tan 2x - cot x = 0 for the interval [0, 2pi)
Use the following identities: cot x = 1/tanx. and tan 2x = (2tanx)/(1-tan2x)
The equation then becomes (2tanx)/(1-tan2x) - 1/(tanx) = 0
Add 1/(tanx) to each side: (2tanx)/(1-tan2x) = 1/(tanx).
Multiply each side by tanx*(1-tan2x): 2tan2x = 1-tan2x.
Combine terms: 3tan2x = 1, divide by 3: tan2x = 3, so tanx = √3 and tanx = -√3.
so x = π/3 in each of the 4 quadrants.