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      <text>4.3.1.3 Pythagoras</text>
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      <text><![CDATA[<div class="HELM_keypoint">
<h4>Key Point</h4>
<p>For any value of <span class="math inline">\(\theta\)</span> <span class="math display">\[\sin^2\theta+\cos^2\theta\equiv1\]</span></p>
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<p>One way of proving the result in the Key Point is to use the definitions of <span class="math inline">\(\sin\theta\)</span> and <span class="math inline">\(\cos\theta\)</span> obtained from the circle of unit radius.</p>

<p>Recall that  <span class="math inline">\(\cos\theta=OQ\)</span>, <span class="math inline">\(\ \sin\theta=OR=QP\)</span>. By Pythagoras’ theorem:<span class="math inline">\((OQ)^2+(QP)^2=(OP)^2=1\)</span></p>

<p>hence <span class="math inline">\(\cos^2\theta+\sin^2\theta=1.\)</span></p>

<p>We have demonstrated the Key Point using an angle <span class="math inline">\(\theta\)</span> in the first quadrant but the result is true for any <span class="math inline">\(\theta\)</span> i.e. it is indeed an identity.</p>]]></text>
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