How Do You Simplify cos(2 * arcsin(2x))?

[jwxie]

Homework Statement

cos(2 * arcsin(2x))

Use a triangle to simplify each expression. Where application, state the range of x's for which the simplification holds.

Homework Equations

cos(2t) = cos^2(t) - sin^2(t) = 1-2sin^2(t) = 2cos^2(t) - 1

The Attempt at a Solution

My attempt was the following

cos(2*arcsin(2x))

let arcsin(2x) = delta (or t)
so cos(2t) = double angle formula

cos2(t) = 1-2sin^2(t)
replace t, and by definition sin(arcsinx) = x
so i think i got 1-2*(2x)^2 = 1-8x^2

please verify for me

thank you

 

[Mark44]

Homework Statement

cos(2 * arcsin(2x))

Use a triangle to simplify each expression. Where application, state the range of x's for which the simplification holds.

Homework Equations

cos(2t) = cos^2(t) - sin^2(t) = 1-2sin^2(t) = 2cos^2(t) - 1

The Attempt at a Solution

My attempt was the following

cos(2*arcsin(2x))

let arcsin(2x) = delta (or t)
so cos(2t) = double angle formula

cos2(t) = 1-2sin^2(t)
replace t, and by definition sin(arcsinx) = x
so i think i got 1-2*(2x)^2 = 1-8x^2

please verify for me

thank you

That's what I get.