Buktikanlah identitas trigonometri berikut. (tan α + sin α)(1 - cos α)= sin² α tan α

<p>Pembuktian seperti uraian diberikut</p><p>&nbsp;</p><p>Ingat!</p><p>tan α = sin α/cos α</p><p>sin²α = (1 - cos²α)</p><p>&nbsp;</p><p>Buktikan</p><p>(tan α + sin α)(1 - cos α)= sin²α tan α</p><p>&nbsp;</p><p>Perhatikan perhitungan berikut</p><p>(tan α + sin α)(1 - cos α)</p><p>= tan α +sin α - tan α cos α - sin α cos α&nbsp;</p><p>= tan α &nbsp;+ sin α &nbsp;- sinα /cosα . cosα &nbsp;- sin α &nbsp;cos α&nbsp;</p><p>= tan α &nbsp;+ sin α &nbsp;- sin α &nbsp;- sin α &nbsp;cos α&nbsp;</p><p>= tan α - sin α &nbsp;cos α&nbsp;</p><p>= (sin α /cos α ) - sin α cos α&nbsp;</p><p>= (sin α /cos α ) - (sin α cos² α )/(cos α)</p><p>= (sin α/cos α)(1 - cos² α)</p><p>= tan α . sin² &nbsp;α</p><p>= sin² α tan α<br>&nbsp;</p><p>Dengan demikian terbukti bahwa (tan α + sin α)(1 - cos α)= sin² α tan α.</p>