Cot 2x csc 2x

Cot 2x csc 2x

Input
cot(2 x) csc(2 x)
Alternate form assuming x is real
(2 sin(2 x) sin(4 x))/(cos(4 x) – 1)^2
Roots
x = 1/4 (2 pi n + pi), n element Z
Series expansion at x=0
1/(4 x^2) – 1/6 – (7 x^2)/30 – (31 x^4)/189 + O(x^6)
(Laurent series)
Derivative
d/dx(cot(2 x) csc(2 x)) = -(cos(4 x) + 3) csc^3(2 x)
Indefinite integral
integral cot(2 x) csc(2 x) dx = -1/4 csc(x) sec(x) + constant

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