How do you prove $arccos(x/2) + arctan(x) = pi/2$ ?

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Answer 1 · 2016-05-24T21:31:24

You can't prove it. It is not always true.

For example, with $x=1$ , we get

$arccos(1/2)+arctan(1) = pi/3+pi/4 = (7pi)/12 != pi/2$

It is true only for $x=0$ , $x=sqrt3$ , and $x=-sqrt3$ .

How do you prove arccos(x/2) + arctan(x) = pi/2arccos(x/2) + arctan(x) = pi/2?