SOLUTION: Find all solutions between : 0 less than or equal to Theta which is less than 2pi 4csc(x) = csc^5(x)

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Question 1072254: Find all solutions between : 0 less than or equal to Theta which is less than 2pi
4csc(x) = csc^5(x)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
csc%5E5%28x%29-4csc%28x%29=0
csc%28x%29%28csc%5E4%28x%29-4%29=0
highlight_green%28csc%28x%29%28csc%5E2%28x%29-2%29%28csc%5E2%28x%29%2B2%29=0%29
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At least one of the factors must be 0.

csc%28x%29=1%2Fsin%28x%29=0, not useful; not possible.


csc%5E2%28x%29-2=0
csc%5E2%28x%29=2
1%2F%28sin%5E2%28x%29%29=2
sin%5E2%28x%29=1%2F2
sin%28x%29=0%2B-+sqrt%282%29%2F2
system%28x=45%2Adegrees%2Cor%2Cx=135%2Adegrees%29
or
system%28x=225%2Adegree%2Cor%2Cx=315%29