Solve the equation. (Find all solutions of the equation in the interval [0, 2𝜋). Enter your answers as a comma-separated list.) 4 tan(2x) − 4 cot(x) = 0

Answer 1

Using the double angle formula for tan and that cot is 1/tan:

2tan/(1-tan²) - 1/tan = 0 ( the 4 times requires that this part be zero as the 4 cannot make the equation equal to zero.

2tan²x = 1- tan²x.

tan²x = 1/3

tanx = +/- 1/sqrt(3) x = pi/6, 5pi/6, 7pi/6, 11pi/6

Also there is a weirdness in that both terms go to 0 when tanx goes to +/- infinity. This happens at pi/2, 3pi/2

If you plot this equation on DESMOS you can see what the function looks like and that the zeroes are clear.