Tính sin6°° .cos 12° .cos24°.cos 48°.

Trả lời

Lời giải

Đặt A = sin6°.cos12°.cos24°.cos48°
Suy ra A. cos6° = sin6°.cos6°.cos12°.cos24°.cos48°
= \[\frac{1}{2}\]sin12°.cos12°.cos24°.cos48°
= \[\frac{1}{4}\]sin24°.cos24°.cos48° = \[\frac{1}{8}\]sin48°.cos48°

\[ = \frac{1}{{16}}sin96^\circ = \]\[\frac{1}{{16}}cos6^\circ \].

Do đó \[A = \frac{1}{{16}}\].