SOLUTION: show:
cot^2x/1-cos^2x=csc^2x
Algebra.Com
Question 1167515: show:
cot^2x/1-cos^2x=csc^2x
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
show:
cot^2x/1-cos^2x=csc^2x
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If you mean:
cot^2(x)/(1-cos^2(x))=csc^2(x)
cot^2(x)/(sin^2(x))=csc^2(x)
Multiply by sin^2(x)
cot^2(x) = 1
------
That can be solved for x, but you said "show."
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
It looks like you mean:
}{1\,-\,\cos^2(x)}\ =\ \csc^2(x))
And that you are asking to show that this is an identity.
This is unfortunate, because the equation shown is not an identity.
It is only true when \ =\ \pm\sin(x))
which is only true when 
}{\sin^2(x)}}{\sin^2(x)}\ =\ \frac{1}{\sin^2(x)})
}{\sin^2(x)}\cdot{\frac{1}{\sin^2(x)}\ =\ \frac{1}{\sin^2(x)})
}{\sin^2(x)}\ =\ 1)
\ =\ \sin^2(x)\ =\ 1\ - \cos^2(x))
\ =\ \frac{1}{2})
\ =\ \pm\frac{\sqrt{2}}{2})
\ =\ \frac{\pi}{4}\ +\ \frac{n\pi}{2}\,\forall\,n\,\in\,\mathbb{Z})
John
My calculator said it, I believe it, that settles it
I > Ø
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