Jawab:
[tex]\frac{1}{64}[/tex]
Penjelasan dengan langkah-langkah:
Menggunakan identitas:
[tex]\boxed{2sinx cosx = sin2x}[/tex]
cos12 cos24 cos36 cos48 cos72 cos84
[tex]= \frac{(2sin12*cos12)cos24*cos36*cos48*cos72*cos84}{2sin12} \\\\=\frac{2sin24*cos24*cos36*cos48*cos72*cos84}{4sin12} \\\\=\frac{-2sin48*cos48*cos36*cos72*cos(180-84)}{8sin12}\\\\=\frac{-2sin96*cos96*cos36*cos72}{16sin12}\\\\=\frac{-sin192*cos36*cos27}{16sin12}\\ \\=\frac{-sin(180+12)*cos36*cos27}{16sin12}\\\\=\frac{sin12(2sin36cos36)cos72}{32sin12sin16}\\ \\=\frac{2sin72cos72}{64sin36} \\\\=\frac{sin144}{64sin36}\\ \\=\frac{sin(180-144)}{64sin36}\\\\=\frac{1}{64}[/tex]
Jadi, nilai dari cos12 cos24 cos36 cos48 cos72 cos84 adalah [tex]\frac{1}{64}[/tex].
" Life is not a problem to be solved but a reality to be experienced! "
© Copyright 2013 - 2024 KUDO.TIPS - All rights reserved.
Jawab:
[tex]\frac{1}{64}[/tex]
Penjelasan dengan langkah-langkah:
Menggunakan identitas:
[tex]\boxed{2sinx cosx = sin2x}[/tex]
cos12 cos24 cos36 cos48 cos72 cos84
[tex]= \frac{(2sin12*cos12)cos24*cos36*cos48*cos72*cos84}{2sin12} \\\\=\frac{2sin24*cos24*cos36*cos48*cos72*cos84}{4sin12} \\\\=\frac{-2sin48*cos48*cos36*cos72*cos(180-84)}{8sin12}\\\\=\frac{-2sin96*cos96*cos36*cos72}{16sin12}\\\\=\frac{-sin192*cos36*cos27}{16sin12}\\ \\=\frac{-sin(180+12)*cos36*cos27}{16sin12}\\\\=\frac{sin12(2sin36cos36)cos72}{32sin12sin16}\\ \\=\frac{2sin72cos72}{64sin36} \\\\=\frac{sin144}{64sin36}\\ \\=\frac{sin(180-144)}{64sin36}\\\\=\frac{1}{64}[/tex]
Jadi, nilai dari cos12 cos24 cos36 cos48 cos72 cos84 adalah [tex]\frac{1}{64}[/tex].