trigo problem...?

Question

Find all the angles between 0 and 360 degrees inclusive which satisfy the equation

(i) 9 tan x = cot x

Please could you also tell me what are the important things or points that I have to look out for so as to make sure that I have done the trigonometry questions correct? Thanks a lot.

Answer 1

9 tan x = 1 / tan x
9 tan ² x = 1
tan ² x = 1 / 9
tan x = ± 1 / 3
x = 18.4 ° , 161.6 ° , 198.4 ° , 341.6 °

Answer 2

This is
9 tan(x) = cot(x)
9 (1 / cot(x)) = cot(x)
9 = cot^2(x)
cot(x) = ±3
So x = cot^-1(3), cot^-1(-3).
You should have answers for all 4 quadrants.