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Câu hỏi: \({{\sin {\pi \over {15}}\cos {\pi \over 10} + \sin {\pi \over {10}}\cos {\pi \over 15}} \over {\cos {{2\pi } \over {15}}\cos {\pi \over {5}} - \sin {{2\pi } \over {15}}\sin {\pi \over {5}}}}\) bằng:
\((A) \sqrt 3 (B) 1 \)
\((C) - 1 (D) {1 \over 2}\)
\((A) \sqrt 3 (B) 1 \)
\((C) - 1 (D) {1 \over 2}\)
Lời giải chi tiết
Ta có:
\(\eqalign{
& {{\sin {\pi \over {15}}\cos {\pi \over 10} + \sin {\pi \over {10}}\cos {\pi \over 15}} \over {\cos {{2\pi } \over {15}}\cos {\pi \over {5}} - \sin {{2\pi } \over {15}}\sin {\pi \over {5}}}} \cr &= {{\sin ({\pi \over {15}} + {\pi \over {10}})} \over {\cos ({{2\pi } \over {15}} + {\pi \over 5})}} \cr
& = {{\sin {\pi \over 6}} \over {\cos {\pi \over 3}}} = 1 \cr} \)
Chọn (B)
Ta có:
\(\eqalign{
& {{\sin {\pi \over {15}}\cos {\pi \over 10} + \sin {\pi \over {10}}\cos {\pi \over 15}} \over {\cos {{2\pi } \over {15}}\cos {\pi \over {5}} - \sin {{2\pi } \over {15}}\sin {\pi \over {5}}}} \cr &= {{\sin ({\pi \over {15}} + {\pi \over {10}})} \over {\cos ({{2\pi } \over {15}} + {\pi \over 5})}} \cr
& = {{\sin {\pi \over 6}} \over {\cos {\pi \over 3}}} = 1 \cr} \)
Chọn (B)