Which trigonometric functions do not have real zeros?

Answer 1

The trigonometric functions that do not have real zeros are the cosine function ((\cos(x))) and the secant function ((\sec(x))). The cosine function is never zero for (x) values that correspond to integer multiples of (\frac{\pi}{2}), while the secant function, being the reciprocal of cosine, is undefined at those points. Therefore, both functions do not intersect the x-axis in the real number system.