SOLUTION: simplify sqrt x^2-9 as much as possible after substituting 3csc theta I can only get to sqrt{3csc^2}

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Question 851501: simplify sqrt x^2-9 as much as possible after substituting 3csc theta
I can only get to sqrt{3csc^2} - 9. Do I FOIL?
Found 2 solutions by stanbon, harpazo:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
simplify sqrt x^2-9 as much as possible after substituting 3csc theta
I can only get to sqrt{3csc^2} - 9}
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sqrt[3(csc^2(t)-3)]
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= sqrt[3(csc(t)-sqrt(3))(csc(t+sqrt(3))
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Cheers,
Stan H.
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Answer by harpazo(655) (Show Source):
You can put this solution on YOUR website!

I will use t for theta. No foil needed.
sqrt{(3csct)^2-9}
sqrt{9*csc^2 t - 9}
In the radical, factor out 9.
sqrt{9(csc^2 t - 1)}
Separate into two integrals.
sqrt(9)*sqrt(csc^2 t - 1)
3*sqrt{(csct-1)(csct+1)
Did you follow?

SOLUTION: simplify sqrt x^2-9 as much as possible after substituting 3csc theta I can only get to sqrt{3csc^2} - 9. Do I FOIL?