It is impossible to obtain exact values for the inverse seca

It is impossible to obtain exact values for the inverse secant function. True or False?

Solution

True.

Because if inverse secant or cosecant functions are defined then inverse cosine and inverse sine functions should also be defined. As they are just reciprocals of them.

But when we take y= sec^-1x

then its domain is (-infinite, -1] U [1,infinite)

But if one has to say that cos^-1x should also be defined then their domain should match but they mismatches...as domain of cos^-1x is [-1,1].