\({{\sin {\pi \over {15}}\cos {\pi \over 10} + \sin {\pi \over {10}}\cos {\pi \over 15}} \over {\cos {{2\pi } \over {15}}\cos {\pi \over {15}} – \sin {{2\pi } \over {15}}\sin {\pi \over {15}}}}\) bằng:
\((A)\,\sqrt 3 \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\;(B)\,1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\)
\((C)\, – 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(D)\, {1 \over 2}\)
Đáp án
Ta có:
\(\eqalign{
& {{\sin {\pi \over {15}}\cos {\pi \over 10} + \sin {\pi \over {10}}\cos {\pi \over 15}} \over {\cos {{2\pi } \over {15}}\cos {\pi \over {15}} – \sin {{2\pi } \over {15}}\sin {\pi \over {15}}}} = {{\sin ({\pi \over {15}} + {\pi \over {10}})} \over {\cos ({{2\pi } \over {15}} + {\pi \over 5})}} \cr
& = {{\sin {\pi \over 6}} \over {\cos {\pi \over 3}}} = 1 \cr} \)
Chọn (B)