How do you simplify $Sin(arccos x)$ ?

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Answer 1 · 2016-06-24T03:13:20

sin x

arccos x --> arc x
sin (arccos x) --> sin x

Answer 2 · 2016-06-24T04:32:52

$+-sqrt(1-x^2)$ .

Let a = arc cos x. Then, cos a = x = cos (-a).

So, a might be in anyone of the four quadrants.

Accordingly, the given expression

$sin a=+-sqrt(1-cos^2 a)=+-sqrt(1-x^2)$ .

How do you simplify Sin(arccos x)Sin(arccos x)?