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Solve tan 2x - cot x = 0

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1 Answer

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.

Comments

AAARG!  I don't believe I made that mistake.
 
tanx = 1/√3 and x = -1/√3  so x = π/6 in each of the 4 quadrants.  Sorry.