Question

How do you find an equivalent algebraic expression for the composition cos(arcsin(x))?

Answer 1

`sqrt(1-x^2)`.

Explanation:

Since `cos^2(x)=1-sin^2(x)`, you have that `cos(x)=\pm\sqrt(1-sin^2(x))`. So, your expression becomes

`sqrt(1-sin^2(arcsin(x))`

And since `sin(arcsin(x))=x`, then `sin^2(arcsin(x))=x^2`.

So, your expression becomes `sqrt(1-x^2)`.