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Math Help - Proof of cos(arcsin(x))

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    Proof of cos(arcsin(x))

    Hello, I was wondering if someone could help me with the proof of cos(arcsin(x))=sqrt(1-x^2). I'm a little confused, I was using cos=sqrt(1-x^2) and arcsin=1/(sqrt(1-x^2)) and getting no where. A trigonometric proof isn't needed but if it's the only way then that's fine. Thanks for all help!
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    Quote Originally Posted by Dudealadude View Post
    Hello, I was wondering if someone could help me with the proof of cos(arcsin(x))=sqrt(1-x^2). I'm a little confused, I was using cos=sqrt(1-x^2) and arcsin=1/(sqrt(1-x^2)) and getting no where. A trigonometric proof isn't needed but if it's the only way then that's fine. Thanks for all help!
    let y = \arcsin(x)

    this can also be written as ...

    \displaystyle \sin(y) = x = \frac{x}{1} = \frac{opposite \, side}{hypotenuse}

    \displaystyle \cos[\arcsin(x)] = \cos(y) = \frac{adjacent \, side}{hypotenuse} = \frac{\sqrt{1 - x^2}}{1} = \sqrt{1 - x^2}
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