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

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

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simplify sec(arctan(2/x))

simplify

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

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

Solution steps

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

Use the following identity:

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

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

Simplify

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

tan (θ) 1 - sin^{2} (θ)

sin (t + 2 π) \cdot sec (t + 2 π)

\frac{2 csc ( 2 t )}{csc ( - t )}

cos (27 0^{\circ} - θ)

- cos (n (- π))