Question

what is the algebraic expression of tan(arccos(x))

Answer 1

1) draw a right triangle

Answer 2

2) label the adjacent side \(x\) and the hypotenuse \(1\) so that the cosine of the angle \(\theta\) is \(x\) i.e.
\[\theta=\arccos(x)\]

Answer 3

3) find the missing side by pythagoras or memory
it is \(\sqrt{1-x^2}\)

Answer 4

4) write the tangent , which is opposite over adjacent