How do you simplify $tan (a r c sec x)$ $tan (arcsec x)$ ?

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Answer 1 · 2016-08-31T08:07:54

$\pm \sqrt{x^{2} - 1}, x \in (- \infty, - 1] or [1, \infty)$ $+-sqrt(x^2-1), x in (-oo, -1] or [1, oo)$ .

Let $a = a r c sec x \in Q 1 or Q 2$ $a = arc sec x in Q1 or Q2$ , for principal value of a, wherein tan

is either positive or negative. Then

$sec a = x \in (- \infty, - 1] or [1, \infty)$ $sec a = x in (-oo, -1] or [1, oo)$ .

The given expression is

$tan a = \pm \sqrt{{sec}^{2} a - 1} = \pm \sqrt{x^{2} - 1}$ $tan a = +-sqrt(sec^2a-1)=+-sqrt(x^2-1)$ ,

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

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