Chapter 7 - Section 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas - 7.3 Exercises - Page 561: 46

$1-2x^2$

Step 1. Let $u=sin^{-1}x$, by definition of inverse function, we have $sin(u)=x$ Step 2. Use the Double-Angle Formula, we have $cos(2u)=1-2sin^2(u)=1-2x^2$ Step 3. Thus the original expression $cos(2sin^{-1}x)=cos(2u)=1-2x^2$