Question

Need help finding answer to sin(2sin^-1(x)) in terms of x.

Answer 1

\[\sin(2\theta)=2\sin(\theta)\cos(\theta)\]

Answer 2

here \(\theta=\sin^{-1}(x)\) making
\[\sin(\theta)=\sin(\sin^{-1}(x))=x\]

Answer 3

and
\[\cos(\theta)=\cos(\sin^{-1}(x))=\sqrt{1-x^2}\]

Answer 4

multiply them together, stick a 2 in front of them and you are done

Answer 5

So that would be 2xsqrt(1-x^2)?

Answer 6

yes

Answer 7

Thank you so much :)