Write the expression `cos(2*sin^-1(x))` as an algebraic expression in x for x > 0?  

Expert Answers
justaguide eNotes educator| Certified Educator

The expression `cos(2*sin^-1(x))` has to be expressed as an algebraic expression in x.

`cos(2*sin^-1(x))`

=> `1 - 2*sin^2(sin^-1(x))`

=> `1 - 2*(sin(sin^-1(x))^2`

=> `1 - 2*x^2`

The expression `cos(2*sin^-1(x))` can be written as `1 - 2*x^2`