Bài 63 trang 219 SGK Đại số 10 Nâng cao

Đề bài

\(\cos {\pi  \over {12}}\cos {{7\pi } \over {12}}\) bằng:

\((A)\,{{\sqrt 3 } \over 2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(B)\,{{\sqrt 3 } \over 4}\)

\((C)\,{1 \over 2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\;\;\;\;\;\;\;(D)\, - {1 \over 4}\)

Lời giải chi tiết

Ta có:

\(\cos {\pi  \over {12}}\cos {{7\pi } \over {12}} \)

\(\begin{array}{l}
= \frac{1}{2}\left[ {\cos \left( {\frac{\pi }{{12}} + \frac{{7\pi }}{{12}}} \right) + \cos \left( {\frac{\pi }{{12}} - \frac{{7\pi }}{{12}}} \right)} \right]\\
= \frac{1}{2}\left( {\cos \frac{{2\pi }}{3} + \cos \left( { - \frac{\pi }{2}} \right)} \right)\\
= \frac{1}{2}\left( { - \frac{1}{2} + 0} \right)\\
= - \frac{1}{4}
\end{array}\)

Chọn D

Loigiaihay.com