cos ( 2sin-¹ x ) = 1 - 2x²
cos (2 a) = 1 - 2 sin²a - 1 donc cos ( 2sin-¹ x ) = 1 - 2 sin²(sin-¹ x) = 1 - 2 x²

cosec²(x) - cot(x) • cosec(x) = 1/sin²(x) - cos(x)/sin²(x) = (1 - cos x)/sin² x =
(1 - cos x) / (1 - cos² x) = (1 - cos x) / [(1 - cos x) (1/ 1+ cos(x))] = 1/ 1+ cos(x)