cotan² A / cosec A = cosec A - sin A

<p><strong>Pembahasan</strong></p><p>&nbsp;</p><p>Buktikan:</p><p>cotan² A/cosec A = cosec A - sin A</p><p>&nbsp;</p><p>cotan A = 1/tan A</p><p>cosec A = 1/sin A</p><p><i>Ingat: cos²A + sin²A = 1</i></p><p>&nbsp;</p><p>maka ubah persamaan tsb menjadi</p><p>&nbsp;</p><p>cotan² A/cosec A &nbsp;</p><p>&lt;=&gt; 1/tan²A × sin A &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</p><p>&lt;=&gt; (cos²A/sin²A) × sin A &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;</p><p>&lt;=&gt; ((1 - sin²A)/sin A)&nbsp;</p><p>&lt;=&gt; 1/sin A - sin²A/sin A</p><p>&lt;=&gt; cosec A - sin A&nbsp;</p><p>----&gt; <strong>terbukti</strong></p>