What is cos(arctan(x 1/3)) ?

The solution to cos(arctan(x 1/3)) is (3sqrt(9+x^2))/(9+x^2)

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simplify cos(arctan(x 1/3))

simplify

cos (arctan (x \frac{1}{3}))

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

Solution steps

cos (arctan (x \frac{1}{3}))

Use the following identity:

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

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

Simplify

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

2 + sin (x - \frac{π}{2})

3 sin (8 x + \frac{π}{2})

cos (\frac{2 π}{105} x - y)

csc (θ - \frac{3 π}{2})

sin (54 0^{\circ} - θ)

What is cos(arctan(x 1/3)) ?
The solution to cos(arctan(x 1/3)) is (3sqrt(9+x^2))/(9+x^2)