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Simplify trigno expression

  • Thread starter jwxie
  • Start date
  • #1
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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
 

Answers and Replies

  • #2
33,171
4,858

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.
 

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