Bài tập 47 trang 215 SGK Toán 10 NC

Bài tập 47 trang 215 SGK Toán 10 NC

a)

\(\begin{array}{*{20}{l}}
\begin{array}{l}
\cos {10^0}\cos {50^0}\cos {70^0}\\
 = \cos {10^0}\left[ {\frac{1}{2}\left( {\cos {{120}^0} + \cos {{20}^0}} \right)} \right]
\end{array}\\
{ =  - \frac{1}{4}\cos {{10}^0} + \frac{1}{2}\cos {{10}^0}\cos {{20}^0}}\\
\begin{array}{l}
 =  - \frac{1}{4}\cos {10^0} + \frac{1}{4}\left( {\cos {{30}^0} + \cos {{10}^0}} \right)\\
 = \frac{1}{4}\cos {30^0} = \frac{{\sqrt 3 }}{8}
\end{array}\\
\begin{array}{l}
 \Rightarrow \cos {10^0}\cos {50^0}\cos {70^0}\\
 = \sin {20^0}\sin {40^0}\sin {80^0} = \frac{{\sqrt 3 }}{8}
\end{array}
\end{array}\)

b)

\(\begin{array}{*{20}{l}}
\begin{array}{l}
\sin {10^0}\sin {50^0}\sin {70^0}\\
 = \frac{1}{2}\left( {\cos {{20}^0} - \cos {{120}^0}} \right)\sin {10^0}
\end{array}\\
{ = \frac{1}{4}\sin {{10}^0} + \frac{1}{2}\sin {{10}^0}\cos {{20}^0}}\\
{ = \frac{1}{4}\sin {{10}^0} + \frac{1}{4}\left( {\sin {{30}^0} - \sin {{10}^0}} \right)}\\
{ = \frac{1}{4}\sin {{30}^0} = \frac{1}{8}}\\
\begin{array}{l}
 \Rightarrow \sin {10^0}\sin {50^0}\sin {70^0}\\
 = \cos {20^0}\cos {40^0}\cos {80^0} = \frac{1}{8}
\end{array}
\end{array}\)

-- Mod Toán 10