2cscx

2cscx

Input
2 csc(x)
Alternate form assuming x is real
-(4 sin(x))/(cos(2 x) – 1)
Roots
(no roots exist)
Series expansion at x=0
2/x + x/3 + (7 x^3)/180 + (31 x^5)/7560 + O(x^6)
(Laurent series)
Derivative
d/dx(2 csc(x)) = -2 cot(x) csc(x)
Indefinite integral
integral 2 csc(x) dx = 2 log(sin(x/2)) – 2 log(cos(x/2)) + constant
Local maxima
max{2 csc(x)} = -2 at x = 2 pi n – pi/2 for integer n
Local minima
min{2 csc(x)} = 2 at x = 2 pi n + pi/2 for integer n

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