What is sec(arctan(2x)) ?

The solution to sec(arctan(2x)) is sqrt(1+4x^2)

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simplify sec(arctan(2x))

simplify

sec (arctan (2 x))

1 + 4 x^{2}

Solution steps

sec (arctan (2 x))

Use the following identity:

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

= 1 + (2 x)^{2}

Simplify

= 1 + 4 x^{2}

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