Do you mean Tan(2x) ‒ Cot(2x) = 0?
If so, recall that Cot(w) = 1/Tan(w), so the equation becomes
Tan(2x) ‒ 1/Tan(2x) = 0 \\ clear the denominators by multiplying both sides by Tan(2x)
Tan²(2x) ‒ 1 = 0 as long as Tan(2x) exists and ≠ 0
Tan²(2x) = 1 so Tan(2x) = -1 or Tan(2x) = 1
Therefore, 2x = 45° or x = 22.5° or 2x = -45° or x = -22.5°
There are many other values of x that work but not between -180° and 180°.
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