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

- 2 sin (x - \frac{π}{4}) + 1

cos (θ^{1} + θ^{2})

4 sin (4 5^{\circ} + x) + 3

sin (arccos (sin (x)))

- sin (2 x + \frac{π}{4})