Tentukan nilai dari : 2 sin 75⁰ cos 15⁰ + 2 cos 105⁹ sin 75⁰

<p>Nilai dari 2 sin 75° cos 15° + 2 cos 105° sin 75° adalah ½ (√3 + 1).</p><p>&nbsp;</p><p>Rumus yang digunakan</p><ul><li>2 sin x cos y = sin (x + y) + sin (x - y)</li><li>2 cos x sin y = sin (x + y) - sin (x - y)</li></ul><p>&nbsp;</p><p><strong>Diketahui</strong></p><p>2 sin 75° cos 15° + 2 cos 105° sin 75°</p><p><strong>Ditanyakan</strong></p><p>Nilai perkalian trigonometri tersebut = ... ?</p><p><strong>Jawaban</strong></p><p>2 sin 75° cos 15° = sin (75° + 15°) + sin (75° - 15°)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= sin 90° + sin 60°</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= 1 + ½ √3</p><p>2 cos 105° sin 75° = sin (105° + 75°) - sin (105° - sin 75°)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= sin 180° - sin 30°</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= 0 - ½</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = -½</p><p>Jadi <strong>nilai</strong> dari <strong>2 sin 75° cos 15° + 2 cos 105° sin 75°</strong> adalah</p><p>= (1 + ½ √3) + (-½)</p><p>= 1 + ½ √3 - ½</p><p>= ½ √3 + 1 - ½</p><p>= ½ √3 + ½</p><p>= ½ (√3 + 1)</p>