Question

How do you simplify `cos(2 arcsin x)`?

Answer 1

`cos(2arcsin(x))=1-2x^2`

Explanation:

Using `cos(a+b)=Cos(a) Cos(b) - Sin(a) Sin(b)`.

If `a = b` then

`cos(2a)=1-2sin^2(a)`

so

`cos(2arcsin(x))=1-2x^2`