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Math Help - [SOLVED] Simplification

  1. #1
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    [SOLVED] Simplification

    I need help understanding the question: simplify the expression cos^2(arcsin t) using the property that inverses "undo" each other.
    I get that arcsin(t)=sin^-1(t) and that that would be the opposite of sin(t). But cos(t) isn't the opposite of sin(t), is it?
    Yes, I do know what simplifying is, but I'm not sure how to do it here.
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  2. #2
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    Quote Originally Posted by Dotdash13 View Post
    I need help understanding the question: simplify the expression cos^2(arcsin t) using the property that inverses "undo" each other.
    I get that arcsin(t)=sin^-1(t) and that that would be the opposite of sin(t). But cos(t) isn't the opposite of sin(t), is it?
    Yes, I do know what simplifying is, but I'm not sure how to do it here.
    \cos^2{x} + \sin^2{x} = 1 so \cos^2{x} = 1 - \sin^2{x}.


    Therefore \cos^2{\arcsin{t}} = 1 - \sin^2{\arcsin{t}} = 1 - t^2.
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