Bài 63: \(\cos {\pi \over {12}}\cos {{7\pi } \over {12}}\) bằng:
\((A)\,{{\sqrt 3 } \over 2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(B)\,{{\sqrt 3 } \over 4}\)
\((C)\,{1 \over 2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\;\;\;\;\;\;\;(D)\, – {1 \over 4}\)
Đáp án
Ta có:
\(\cos {\pi \over {12}}\cos {{7\pi } \over {12}} = {1 \over 2}(cos{{2\pi } \over 3} + \cos {\pi \over 2}) = – {1 \over 4}\)
Chọn D
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Bài 64: \(\sin {{{{90}^0}} \over 4}\cos {{{{270}^0}} \over 4}\) bằng:
\(\eqalign{
& (A)\,{1 \over 2}(1 – {{\sqrt 2 } \over 2})\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(B)\,{1 \over 2}({{\sqrt 2 } \over 2} – 1)\,\,\, \cr
& (C)\,{1 \over 2}(1 + {{\sqrt 2 } \over 2})\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(D)\,\sqrt 2 – 1 \cr} \)
Đáp án
Ta có:
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\(\sin {{{{90}^0}} \over 4}\cos {{{{270}^0}} \over 4} = {1 \over 2}\sin ({90^0} – \sin {45^0}) \)
\(= {1 \over 2}(1 – {{\sqrt 2 } \over 2})\)
Chọn (A)
Bài 65: \({{\cos {{80}^0} – \cos {{20}^0}} \over {\sin {{40}^0}\cos {{10}^0} + \sin {{10}^0}\cos {{40}^0}}}\) bằng:
\(\eqalign{
& (A)\,\,1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(B)\,{{\sqrt 3 } \over 2} \cr
& (C)\,\, – 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(D)\, – {{\sqrt 3 } \over 2} \cr} \)
Đáp án
Ta có:
\({{\cos {{80}^0} – \cos {{20}^0}} \over {\sin {{40}^0}\cos {{10}^0} + \sin {{10}^0}\cos {{40}^0}}} = {{ – 2\sin {{50}^0}\sin {{30}^0}} \over {\sin ({{40}^0} + {{10}^0})}} \)
\(= – 2\sin {30^0} = – 1\)
Vậy chọn C
