Question

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

Answer 1

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

Explanation:

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,`