Find a formula for cos(2arcsinx)

Question

Find a formula for cos(2arcsinx)

Answer 1

I'm not completely sure what you are asking in this question, but let me proceed and see if this makes sense:

Since arcsin x refers to an angle ( let's call it θ ) whose sin is x, then the expression inside the ( ) can be re-written as ( 2θ ), so now our entire expression becomes cos (2θ ). As an identity, cos (2θ ) has 3 variations of its formula. The 3 versions of the double-angle identity formula for cosine are:

1) cos (2θ ) = cos² θ - sin²θ

2) cos (2θ ) = 2cos² θ - 1

3) cos (2θ ) = 1 - 2sin² θ

Again, I'm not sure this is what your question is actually asking, but I hope this helps.

Answer 2