Cot 2x csc 2x
Input |
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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 |