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Thread: Simplify the trig expression

  1. September 9th 2008, 04:27 PM #1
    dm10
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    Simplify the trig expression

    tan(arcsin x)

    sin(arctan x)

    Please Help, I have no idea what to do.
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  2. September 9th 2008, 04:43 PM #2
    mr fantastic
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    Quote Originally Posted by dm10 View Post
    tan(arcsin x)

    sin(arctan x)

    Please Help, I have no idea what to do.
    Let \arcsin x = \theta \Rightarrow x = \sin \theta.

    \tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{x}{\sqrt{1 - x^2}}.

    Therefore \tan (\arcsin x) = \frac{x}{\sqrt{1 - x^2}}.

    Only the positive root is required (why?).


    Try the second one now.
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  3. September 9th 2008, 04:48 PM #3
    Prove It
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    Quote Originally Posted by dm10 View Post
    tan(arcsin x)

    sin(arctan x)

    Please Help, I have no idea what to do.
    Never mind, Mr Fantastic beat me :P
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