What is cos(arctan(x/3)) ?

The solution to cos(arctan(x/3)) is (3sqrt(9+x^2))/(9+x^2)

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simplify cos(arctan(x/3))

simplify

cos (arctan (\frac{x}{3}))

\frac{3 9 + x ^{2}}{9 + x ^{2}}

Solution steps

cos (arctan (\frac{x}{3}))

Use the following identity:

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

= \frac{1 + ( \frac{x}{3} ) ^{2}}{1 + ( \frac{x}{3} ) ^{2}}

Simplify

= \frac{3 9 + x ^{2}}{9 + x ^{2}}

sec (arcsin (x - 1))

cos (27 0^{\circ} - x)

sin (arctan (\frac{1}{x}))

cot (π - θ)

sin (27 0^{\circ} + x)

What is cos(arctan(x/3)) ?
The solution to cos(arctan(x/3)) is (3sqrt(9+x^2))/(9+x^2)