What is sec(arctan(3x)) ?

The solution to sec(arctan(3x)) is sqrt(1+9x^2)

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simplify sec(arctan(3x))

simplify

sec (arctan (3 x))

1 + 9 x^{2}

Solution steps

sec (arctan (3 x))

Use the following identity:

sec (arctan (x)) = 1 + x^{2}

= 1 + (3 x)^{2}

Simplify

= 1 + 9 x^{2}

(4 - 4 sin^{2} (x))

cos (- a - b)

tan (2 θ + 2 θ)

sin (n - π)

36 - 36 sin^{2} (x)