อ้างอิง:
ข้อความเดิมเขียนโดยคุณ BLACK-Dragon
$\sin 3^{\circ} \sin 33^{\circ} \sin 39^{\circ} \sin 69^{\circ} \sin 75^{\circ}=\left(\,\dfrac{\cos 30^\circ+\cos 72^\circ}{2}\right) \left(\,\dfrac{\cos 30^\circ-\cos 36^\circ}{2}\right) \left(\,\dfrac{\sqrt{6}+\sqrt{2}}{4}\right) $
$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \ \ \ \ =\dfrac{\sqrt{6}+\sqrt{2}}{16}\left(\,\dfrac{\sqrt{3}}{2}+\cos 72^\circ \right) \left(\,\dfrac{\sqrt{3}}{2}-\cos 36^\circ\right) $
$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \ \ \ \ =\dfrac{\sqrt{6}+\sqrt{2}}{64}\left(\,2-\sqrt{3}\right) $
$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \ \ \ \ = \dfrac{\sqrt{6}-\sqrt{2}}{64}$
|
$4\left(\,\dfrac{\sqrt{3}}{2}+\cos 72^\circ \right) \left(\,\dfrac{\sqrt{3}}{2}-\cos 36^\circ\right)=\left(\,2-\sqrt{3}\right)$ มายังไงเหรอครับ
