What is csc(arctan(x/5)) ?

The solution to csc(arctan(x/5)) is (sqrt(25+x^2))/x

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simplify csc(arctan(x/5))

simplify

csc (arctan (\frac{x}{5}))

\frac{25 + x ^{2}}{x}

Solution steps

csc (arctan (\frac{x}{5}))

Use the following identity:

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

= \frac{1 + ( \frac{x}{5} ) ^{2}}{( \frac{x}{5} )}

Simplify

= \frac{25 + x ^{2}}{x}

tan (5 π + a)

sin (arctan (x) + arccos (0))

- cos (x - π)

2 cos (\frac{π}{4} - x)

sec (x - \frac{π}{2})