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

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

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simplify cos(arctan(x/5))

simplify

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

\frac{5 25 + x ^{2}}{25 + x ^{2}}

Solution steps

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

Use the following identity:

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

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

Simplify

= \frac{5 25 + x ^{2}}{25 + x ^{2}}

csc (arccot (x))

cos (- πn)

sin (t + \frac{π}{2})

tan (arcsec (3 x))

csc (arctan (x))

What is cos(arctan(x/5)) ?
The solution to cos(arctan(x/5)) is (5sqrt(25+x^2))/(25+x^2)