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

The solution to cos(arctan(x/a)) is (asqrt(a^2+x^2))/(a^2+x^2)

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simplify cos(arctan(x/a))

simplify

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

\frac{a a ^{2} + x ^{2}}{a ^{2} + x ^{2}}

Solution steps

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

Use the following identity:

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

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

Simplify

= \frac{a a ^{2} + x ^{2}}{a ^{2} + x ^{2}}

csc (arccos (\frac{x}{7}))

sec^{3} (\frac{π}{2} - x)

csc (arctan (q))

cos (2 x + \frac{π}{3})

cos (3 t + 3 π)

What is cos(arctan(x/a)) ?
The solution to cos(arctan(x/a)) is (asqrt(a^2+x^2))/(a^2+x^2)