PHẦN II. TỰ LUẬN (3,0 điểm)

 Cho \[\sin \alpha = \frac{4}{5}\]và \[\frac{\pi }{2} < \alpha < \pi \]. Tính \[\cos \alpha \]

Trong \[\left( {ABCD} \right)\], gọi \[E = AC \cap BM\]

Ta có: \[\left\{ \begin{array}{l}E \in AC,AC \subset \left( {SAC} \right)\\E \in BM,BM \subset \left( {SBM} \right)\end{array} \right. \Rightarrow E \in \left( {SAC} \right) \cap \left( {SBM} \right){\rm{ }}\left( 1 \right)\]

Ta có:  \[\left\{ \begin{array}{l}S \in \left( {SAC} \right)\\S \in \left( {SBM} \right)\end{array} \right. \Rightarrow S \in \left( {SAC} \right) \cap \left( {SBM} \right){\rm{ }}\left( 2 \right)\]

Từ \[\left( 1 \right)\] và \[\left( 2 \right)\], ta có: \[SE = \left( {SAC} \right) \cap \left( {SBM} \right)\]

Chọn B

Do \( \Rightarrow \sin \alpha  < 0\).

Ta có: \(\sin \alpha  =  - \sqrt {1 - {{\cos }^2}\alpha }  =  - \frac{{\sqrt 7 }}{4}\).

\(P = \cos \left( {\frac{\pi }{3} - \alpha } \right) = \cos \frac{\pi }{3}.\cos \alpha  + \sin \frac{\pi }{3}.\sin \alpha  = \frac{{3 - \sqrt {21} }}{8}\)