Question

How can I simplify....
tan(arcsin x) ??

Answer 1

tan= sin/cos

Answer 2

Yep, so does it become...

\[\frac{ \sin(\sin^{-1} x) }{ \cos(\sin^{-1} x) }\] ??

Answer 3

and then \[\frac{ x }{ \cos (\sin^{-1}x) }\]

Answer 4

yes

Answer 5

Is that the furthest I can simplify?

Answer 6

i think no

Answer 7

Do have any hints on what I can do?

Answer 8

Drawing triangle would be helpful.

Answer 9

Let there be a triangle with opposite side of \(x\), and hypotenuse of \(1\).

By Pythagorean Theorem, adjacent side would be \(\sqrt{1-x^2}\).



From here, we can see that \(\sin\theta = \dfrac{x}{1} = x\), hence \(\theta = \arcsin(x)\)

Now, what is \(\tan\theta = \tan(\arcsin(x))\)?