What is tan(arcsec(3x)) ?

The solution to tan(arcsec(3x)) is sqrt(9x^2-1)

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simplify tan(arcsec(3x))

simplify

tan (arcsec (3 x))

9 x^{2} - 1

Solution steps

tan (arcsec (3 x))

Use the following identity:

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

= (3 x)^{2} - 1

Simplify

= 9 x^{2} - 1

csc (arctan (x))

sin (x) - sin (- x)

sec (\frac{π}{2} - x)

tan (\frac{3 π}{2} + x)

cos (36 0^{\circ} - x)