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

The solution to sin(arctan(x/2)) is (xsqrt(4+x^2))/(4+x^2)

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simplify sin(arctan(x/2))

simplify

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

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

Solution steps

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

Use the following identity:

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

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

Simplify

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

sec (arcsin (x))

cos (- 2 x)

cos (\frac{3 π}{2} + x)

tan (x - \frac{π}{2})

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

What is sin(arctan(x/2)) ?
The solution to sin(arctan(x/2)) is (xsqrt(4+x^2))/(4+x^2)