What is cos(arctan(x/9)) ?

The solution to cos(arctan(x/9)) is (9sqrt(81+x^2))/(81+x^2)

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simplify cos(arctan(x/9))

simplify

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

\frac{9 81 + x ^{2}}{81 + x ^{2}}

Solution steps

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

Use the following identity:

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

= \frac{1 + ( \frac{x}{9} ) ^{2}}{1 + ( \frac{x}{9} ) ^{2}}

Simplify

= \frac{9 81 + x ^{2}}{81 + x ^{2}}

- 3 cos (\frac{1}{2} x - 2 π)

sin (arcsin (\frac{2 x + 1}{3}))

sin (\frac{- πn}{2})

tan (arcsin (x + 2))

cos (α - \frac{π}{2})

What is cos(arctan(x/9)) ?
The solution to cos(arctan(x/9)) is (9sqrt(81+x^2))/(81+x^2)