nilai eksak dari sin10sin50sin70 adalah

jawab

sin 10 . sin 50 . sin 70 =
= (sin 70. sin 50) (sin 10)
= { -1/2 (-2 sin 70 sin 50)} (sin 10)
= { -1/2 (cos(70+50) -cos(70-50)} (sin 10)
= { -1/2 (cos 120 - cos 20)} sin 10
= { -1/2 (-1/2 - cos 20)} sin 10
= (1/4 + 1/2 cos 20) sin 10
= 1/2 sin 10 + 1/2 cos 20 sin 10
= 1/2 sin 10 + 1/2 (2 cos 20 sin 10))
= 1/2 sin 10 + 1/2 (sin 30 - sin 10)
= 1/2 sin 10 + 1/2 sin 30 - 1/2 sin 10
= 1/2 sin 20
= 1/2 (1/2)
= 1/4