What is sec(arctan(x/2)) ?

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

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simplify sec(arctan(x/2))

simplify

sec (arctan (\frac{x}{2}))

\frac{4 + x ^{2}}{2}

Solution steps

sec (arctan (\frac{x}{2}))

Use the following identity:

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

= 1 + (\frac{x}{2})^{2}

Simplify

= \frac{4 + x ^{2}}{2}

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