Solve tan 2x - cot x = 0

Question

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

Answer 1

Wrong answer. Tan^2(x) should equal 1/3 not 3!!

Answer 2

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.