What is sec(arctan(x/4)) ?

The solution to sec(arctan(x/4)) is (sqrt(16+x^2))/4

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simplify sec(arctan(x/4))

simplify

sec (arctan (\frac{x}{4}))

\frac{16 + x ^{2}}{4}

Solution steps

sec (arctan (\frac{x}{4}))

Use the following identity:

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

= 1 + (\frac{x}{4})^{2}

Simplify

= \frac{16 + x ^{2}}{4}

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