What is cos(arctan(u/4)) ?

The solution to cos(arctan(u/4)) is (4sqrt(16+u^2))/(16+u^2)

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simplify cos(arctan(u/4))

simplify

cos (arctan (\frac{u}{4}))

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

Solution steps

cos (arctan (\frac{u}{4}))

Use the following identity:

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

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

Simplify

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

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What is cos(arctan(u/4)) ?
The solution to cos(arctan(u/4)) is (4sqrt(16+u^2))/(16+u^2)