sin°. sin 40°. sin 60°. sin 80° =
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Jawab:
3 / 16
Penjelasan dengan langkah-langkah:
Identitas trigonometri yang digunakan
2 sin a sin b = sin (a + b) + sin (a - b)
2 cos a sin b = sin (a + b) - sin (a - b)
2 cos a cos b = cos (a + b) + cos (a - b)
-2 sin a sin b = cos (a + b) - cos (a - b)
[tex]\displaystyle \sin 20^{\circ}\sin 40^{\circ}\sin 60^{\circ}\sin 80^{\circ}\\=\frac{\sqrt{3}}{2}~(\sin 80^{\circ}\sin 40^{\circ})\sin 20^{\circ}\\=-\frac{\sqrt{3}}{2}~\frac{1}{2}(\cos 120^{\circ}-\cos 40^{\circ})\sin 20^{\circ}\\=-\frac{\sqrt{3}}{4}\left (- \frac{1}{2}\sin 20^{\circ}-\cos 40^{\circ}\sin 20^{\circ} \right )\\=-\frac{\sqrt{3}}{4}\left [ -\frac{1}{2}\sin 20^{\circ}-\frac{1}{2}(\sin 60^{\circ}-\sin 20^{\circ}) \right ]\\=\frac{3}{16}[/tex]
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