What is cos(arctan(x/2)) ?

The solution to cos(arctan(x/2)) is (2sqrt(4+x^2))/(4+x^2)

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simplify cos(arctan(x/2))

simplify

cos (arctan (\frac{x}{2}))

\frac{2 4 + x ^{2}}{4 + x ^{2}}

Solution steps

cos (arctan (\frac{x}{2}))

Use the following identity:

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

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

Simplify

= \frac{2 4 + x ^{2}}{4 + x ^{2}}

sin (2 x + \frac{π}{2})

sin (- A)

tan (\frac{3 π}{2} - x)

tan (arccos (6 x))

tan (36 0^{\circ} - x)

What is cos(arctan(x/2)) ?
The solution to cos(arctan(x/2)) is (2sqrt(4+x^2))/(4+x^2)