How do you simplify the expression $sin(arctan(x/2))$ ?

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Answer 1 · 2016-06-04T16:23:13

$+-x/sqrt(4+x^2)$

Let a = arc tan(x/2). Then, $tan a = x/2$ . As x is a variable, a could be

in any of the four quadrants.,

Accordingly, the given expression

$sin a= +-x/sqrt(4+x^2)$

How do you simplify the expression sin(arctan(x/2))sin(arctan(x/2))?