Question

How do you simplify `tan (arcsec x)`?

Answer 1

`+-sqrt(x^2-1), x in (-oo, -1] or [1, oo)` .

Explanation:

Let `a = arc sec x in Q1 or Q2`, for principal value of a, wherein tan

is either positive or negative. Then

`sec a = x in (-oo, -1] or [1, oo)` .

The given expression is

`tan a = +-sqrt(sec^2a-1)=+-sqrt(x^2-1)`,

`x in (-oo, -1] or [1, oo)` .