sin 3/4π. sin1/4π + cos 3/4π. cos 1/4 adalah?

Mapel : Matematika
Kelas : X SMA
Bab : Trigonometri

Pembahasan :
Sin 3/4π. sin1/4π + cos 3/4π. cos 1/4π
= Cos (3/4π - 1/4π)
= Cos (2/4π)
= Cos 90°
= 0

Sin 3/4π. sin1/4π + cos 3/4π. cos 1/4π
= sin 3*180/4 . sin 180/4 + cos 3*180/4 . cos 180/4
= sin 135 . sin 45 + cos 135 . cos 45
= sin (90 + 45) . sin 45 + cos (90 + 45) . cos 45
= cos 45 . sin 45 + (-sin 45) . cos 45
= 1/2 akar 2 . 1/2 akar 2 + (-1/2 akar 2) . 1/2 akar 2
= 1/2 - 1/2
= 0