>>40
sin(x) 〜 x - (1/3!)x^3 + (1/5!) x^5 + O(x^7)
= x { 1 - h(x)} とおくと

(1/x) { {1/sin(x)} - (1/x) }= (1/x^2) { h(x)/(1 -h(x))}

h(x)/x^2 〜 (1/3!) - (1/5!)x^2 + O(x^4)

h(x) → 0 (x→0)
だから

(1/x) { {1/sin(x)} - (1/x) } → 1/3!