This is a pun on the phrase 'without a second to lose' meaning you completed a task using every minute of the alotted time. However, 'secant' is used in place of 'second' because it sounds similar and because 'secant' refers to the ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine, which I'm guessing is realted to trigonometry (I never took it)
I finished my trigonometry exam without a secant to lose .