SOLUTION: Solve the equation for solutions over the interval [0,2pi) cot^2 theta= (-5) +4csc theta I believe I have solved to the last step which is where I am stuck. This is what

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Question 671952: Solve the equation for solutions over the interval [0,2pi)
cot^2 theta= (-5) +4csc theta
I believe I have solved to the last step which is where I am stuck.
This is what I have done so far (please forgive all the steps if I do not do them I will get lost and not understand what happened along the way):
0= (-5) +4csc theta - csc^2 theta +1
0= (-5) + 1 + 4csc theta - csc ^2 theta
0= (-4) + 4csc theta - csc^2 theta
0= -csc^2 theta + 4csc theta - 4
0= (csc theta -2)(csc theta +2)
Set both to zero:
csc theta-2 = 0
csc theta = 2 (this is where I am stuck...what next?)
csc theta+2=0
csc theta = -2 (again stuck here)
Thank you in advance :)
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
Solve the equation for solutions over the interval [0,2pi)
cot^2 theta= (-5) +4csc theta
use x for theta
cot^2x=-5+4cscx
cos^2x/sin^2x=-5+4/sinx
multiply both sides by sin^2x
cos^2x=-5sin^2x+4sinx
1-sin^2x=-5sin^2x+4sinx
4sin^2x-4sinx+1=0
(2sinx-1)(2sinx-1)=0
2sinx-1=0
sinx=1/2
x=π/6, 5π/6 (multiplicity 2)