Inverse Trigonometric Functions Arcsec and Arccosec

The papers [1], [2], [16], [3], [12], [17], [13], [5], [8], [11], [14], [4], [6], [7], [10], [15], and [9] provide the notation and terminology for this paper. In this paper x, r denote real numbers. The following propositions are true: (1) [0, π2 [⊆ dom (the function sec). (2) ]π2 , π] ⊆ dom (the function sec). (3) [−π2 , 0[⊆ dom (the function cosec). (4) ]0, π2 ] ⊆ dom (the function cosec). (5) The function sec is differentiable on ]0, π2 [ and for every x such that x ∈ ]0, π2 [ holds (the function sec) ′(x) = sinx (cosx)2 . (6) The function sec is differentiable on ]π2 , π[ and for every x such that x ∈ ]π2 , π[ holds (the function sec) ′(x) = sinx (cosx)2 . (7)(i) The function cosec is differentiable on ]−π2 , 0[, and