you divided by cot(x).
you can not divide by zero. so when you divide by cot(x), you must also set up a second equation:
cot(x) = 0
and then solve this to find the other solutions.
cot (x) - cot^2 (x) = 0 x E [0,2pi]
cot (x) = cot^2(x)
cot (x) = 1
tan (x) = 1
x = tan-1(1)
x = pi/4 + pi*n
I get {pi/4, 5pi/4} but the answer is {pi/2, 3pi/2, pi/4, 5pi/4}
In a lot of these types of questions, I keep getting half the solutions, is there a universal method that would allow me to always find all the possible values no matter the identity?
(I don't know if "identity" is the right word for this since x can't be any value but I don't know what else to call it)
Thanks in advance!