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

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Answer 1 · 2016-08-31T08:07:54

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

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

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

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

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