Posted by shinel on Friday, May 27, 2011 at 3:37pm.
find the exact zeros of the function in the interval [0, 2π)
2 cot squared x + 3 csc x=0

trig  Reiny, Friday, May 27, 2011 at 7:42pm
We know that
1 + cot^2 Ø = csc^2 Ø
so our equation is
2(csc^ x  1) + 3csc x = 0
2 csc^2 x + 3csc x  2 = 0
(2cscx 1)(cscx + 2) = 0
cscx = 1/2 or cscx = 2
or
sinx = 2 (not possible) or sinx = 1/2
so x must be in III or IV
x = 7π/6 or 11π/6