How do you simplify $tan(arccos(x/3))$ ?

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Answer 1 · 2016-08-02T16:19:15

$sqrt (9-x^2)/x, -3<=x<=3$ .

Let $a = arccos (x/3) in Q1 or Q2, -1<=x/3<=1$ , and so, $-3 <=x <= 3$

Then, $cos a = x/3, sin a = sqrt(1-cos^2 a)= sqrt(1-x^2/9)$ ,

Now, the given expression is

$tan a =sin a/cos a$

$=sqrt (9-x^2)/x,$

How do you simplify tan(arccos(x/3))tan(arccos(x/3))?