Nhân $\sin 10$ vào 2 vế ta có
$M.\sin 10 = \sin 10 \times \cos 10 \times \cos 20 \times \cos 40 \times \cos 80$
$= \dfrac{1}{2} \sin 20 \times \cos 20 \times \cos 40 \times \cos 80$
$= \dfrac{1}{4} \sin 40 \times \cos 40 \times \cos 80$
$= \dfrac{1}{8} \sin 80 \times \cos 80$
$= \dfrac{1}{16} \sin 160$
$= \dfrac{1}{16} \sin 20$
$= \dfrac{1}{16} . 2\sin 10 \cos 10$
$= \dfrac{1}{8} . \sin 10 \cos 10$
Suy ra
$ M = \dfrac{1}{8} \cos 10$
Vậy $ M = \dfrac{1}{8} \cos 10$
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