Csc^2 – 1

Csc^2 – 1

Input
csc^2(x) – 1
Alternate form assuming x is real
(4 sin^2(x))/(cos(2 x) – 1)^2 – 1
Roots
x = 1/2 (2 pi n + pi), n element Z
Series expansion at x=0
1/x^2 – 2/3 + x^2/15 + O(x^4)
(Laurent series)
Derivative
d/dx(csc^2(x) – 1) = -2 cot(x) csc^2(x)
Indefinite integral
integral (-1 + csc^2(x)) dx = -x – cot(x) + constant

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