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

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

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simplify sec(arctan(y/2))

simplify

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

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

Solution steps

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

Use the following identity:

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

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

Simplify

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

tan (arcsin (X))

tan (\frac{π}{2} - \frac{x}{2})

sin (\frac{π}{2} + arccos (x))

sin (w (t - \frac{π}{w}))

- \frac{sin ( - nπ )}{n ^{2}}