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

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

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simplify csc(arctan(4/x))

simplify

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

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

Solution steps

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

Use the following identity:

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

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

Simplify

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

tan^{2} (\frac{π}{2} + x)

cos (\frac{π}{2} - \frac{π t}{2})

cos (arcsin (\frac{x}{9}))

cos (2 (- x))

cos (2 x - \frac{5 π}{6})