What is tan(arcsec(e^x)) ?

The solution to tan(arcsec(e^x)) is sqrt(e^{2x)-1}

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simplify tan(arcsec(e^x))

simplify

tan (arcsec (e^{x}))

e^{2 x} - 1

Solution steps

tan (arcsec (e^{x}))

Use the following identity:

tan (arcsec (x)) = x^{2} - 1

= (e^{x})^{2} - 1

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= e^{2 x} - 1

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