How do you get 4 answers in this equation?

Question

cot^2X + 3 cot X =1

can you please solve it for me, and tell me how you get multiple answers?

It is cot squared X + 3 times cot x=1

Iced, you answered my question. Thank you very much. Can I have your e-mail, so I can shoot you an e-mail if I run into some trouble?

I still do not get how sometimes I will get like 5 answers. How do you enter this stuff into your calculator too? For example, cos 3x=4/5. How do you find the answers to the problem?

Answer 1

1. it is quadratic, so two answers
2. cot is repeats over pi, so two answers for each answer above

for 1. let y = cot(x) so you have y^2 + 3y -1 =0 and use quadratic equation to solve for two solutions.

for 2. look at the y = cot(x) curve and you should find two solutions for each of the solutions above

Answer 2

cot^2x+3cotx=1 =>cot^2+3cotx-1=0 factoring
cotx =[-3 plus or minus (9+4)]/2=[-3(+or-)(13)]/2
cot is positive in thefirst and third quadrants so there will be four solutions based on this
e.g.if cotx=(+or-)1 then x can be 45,135,225 and 315 all in degrees

Answer 3

there's something off in how you typed it

is it cot (2x) = 3 cot x = 1 ?