How do you simplify tan (arcsec x)?

Aug 31, 2016

$\pm \sqrt{{x}^{2} - 1} , x \in \left(- \infty , - 1\right] \mathmr{and} \left[1 , \infty\right)$ .

Explanation:

Let $a = a r c \sec x \in Q 1 \mathmr{and} Q 2$, for principal value of a, wherein tan

is either positive or negative. Then

$\sec a = x \in \left(- \infty , - 1\right] \mathmr{and} \left[1 , \infty\right)$ .

The given expression is

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

$x \in \left(- \infty , - 1\right] \mathmr{and} \left[1 , \infty\right)$ .