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Math Help - Why does tan^2 y = x

  1. #1
    Member Furyan's Avatar
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    Why does tan^2 y = x^2

    Hello,

    I continue to struggle with trig.

    The question is:

    Given that  x = \tan y show that \dfrac{dy}{dx} = \dfrac{1}{1 + x^2}.

    The answer given, most of which I follow, is:

    \dfrac{d}{dy} (\tan y) = \sec^2 y

    Taking the reciprocal of both sides.

    \dfrac{dy}{dx} = \dfrac{1}{sec^2 y}

    \dfrac{dy}{dx} = \dfrac{1}{1 + \tan^2 y}

    Hence, and this is the bit I don't get.

    \dfrac{dy}{dx} = \dfrac{1}{1 + x^2}

    It's bound to be something I'm supposed to know, something basic, but why is \tan^2 y = x^2

    Thanks
    Last edited by Furyan; August 28th 2012 at 04:33 PM.
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: Why does tan^2 y = x

    Quote Originally Posted by Furyan View Post
    Hello,

    I continue to struggle with trig.

    The question is:

    Given that  x = \tan y show that \dfrac{dy}{dx} = \dfrac{1}{1 + x^2}.

    The answer given, most of which I follow, is:

    \dfrac{d}{dy} (\tan y) = \sec^2 y

    Taking the reciprocal of both sides.

    \dfrac{dy}{dx} = \dfrac{1}{sec^2 y}

    \dfrac{dy}{dx} = \dfrac{1}{1 + \tan^2 y}
    You have been given x = tan(y). Then by squaring both sides: tan^2(y) = x^2.

    -Dan
    Thanks from Furyan
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