1-secx

1-secx

Input
1 – sec(x)
Alternate form assuming x is real
1 – (2 cos(x))/(cos(2 x) + 1)
Roots
x = 2 pi n, n element Z
Series expansion at x=0
-x^2/2 – (5 x^4)/24 – (61 x^6)/720 + O(x^7)
(Taylor series)
Derivative
d/dx(1 – sec(x)) = tan(x) (-sec(x))
Indefinite integral
integral (1 – sec(x)) dx = x + log(cos(x/2) – sin(x/2)) – log(sin(x/2) + cos(x/2)) + constant
Local maxima
max{1 – sec(x)} = 0 at x = 2 pi n for integer n
Local minima
min{1 – sec(x)} = 2 at x = 2 pi n + pi for integer n

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