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<quiz>
  <question type="multichoice">
    <name>
      <text>6.2.3.2 tanh^2</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise&nbsp;</p>
<p>Which of the following identities are correct?</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>Note the following</p>
<p> \( 1 - \tanh^2 x = 1 - \dfrac{\sinh^2 x}{\cosh^2 x} = \dfrac{\cosh^2 x - \sinh^2 x}{\cosh^2 x} = \dfrac{1}{\cosh^2 x} = \) \( \rm{sech}^2 \) \(x\). </p>
<p>To see that each of the other identities is incorrect, specify a particular value for \(x\) for which the identity is wrong. Also note that they are inconsistent with the above correct identities. </p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.3333333</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <single>false</single>
    <shuffleanswers>true</shuffleanswers>
    <answernumbering>abc</answernumbering>
    <showstandardinstruction>1</showstandardinstruction>
    <correctfeedback format="html">
      <text>Your answer is correct.</text>
    </correctfeedback>
    <partiallycorrectfeedback format="html">
      <text>Your answer is partially correct.</text>
    </partiallycorrectfeedback>
    <incorrectfeedback format="html">
      <text>Your answer is incorrect.</text>
    </incorrectfeedback>
    <shownumcorrect/>
    <answer fraction="33.33333" format="html">
      <text><![CDATA[<p>\( 1 - \tanh^2x \equiv \sec{\rm h}^2x \)</p>]]></text>
      <feedback format="html">
        <text/>
      </feedback>
    </answer>
    <answer fraction="0" format="html">
      <text><![CDATA[<p>\( 1 - \tanh^2x \equiv \sinh^2x \)<br></p>]]></text>
      <feedback format="html">
        <text/>
      </feedback>
    </answer>
    <answer fraction="0" format="html">
      <text><![CDATA[<p>\( 1 - \tanh^2x \equiv \cosh^2x \)<br></p>]]></text>
      <feedback format="html">
        <text/>
      </feedback>
    </answer>
    <answer fraction="0" format="html">
      <text><![CDATA[<p>\( 1 - \tanh^2x \equiv \dfrac{1}{\sinh^2x} \)<br></p>]]></text>
      <feedback format="html">
        <text/>
      </feedback>
    </answer>
    <answer fraction="33.33333" format="html">
      <text><![CDATA[<p>\( 1 - \tanh^2x \equiv \dfrac{1}{\cosh^2x} \)<br></p>]]></text>
      <feedback format="html">
        <text/>
      </feedback>
    </answer>
    <answer fraction="33.33333" format="html">
      <text><![CDATA[<p>\( 1 - \tanh^2x \equiv \dfrac{\cosh^2x - \sinh^2x}{\cosh^2x}\)</p>]]></text>
      <feedback format="html">
        <text/>
      </feedback>
    </answer>
    <answer fraction="0" format="html">
      <text><![CDATA[<p>\(1 - \tanh^2x \equiv \dfrac{\sinh^2x - \cosh^2x}{\sinh^2x}\)<br></p>]]></text>
      <feedback format="html">
        <text/>
      </feedback>
    </answer>
  </question>
</quiz>
