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高中《代数》上册P193有这样一道例题: 求sin~210°+cos~240°+sin10°cos40°的值。 无独有偶,近几年来,与这道例题类似的考题有 (1)求cos~215°+cos~275°+cos15°cos75°的值。(’90全国高考题) (2)求值:cos~210°+cos~250°-sin~240°sin~280°。(’91全国高中联赛题) (3)求sin~220°+sin~280°+2~(1/3)sin~220°cos80°的值。(’92全国高考题) (4)求cos~210°+sin~240°-cos10°sin40°的值。(’93湖南高中会考题) (5)求sin~220°+cos~250°+sin20°cos50°的值。(’95全国高考题) 从例题、考题所显示的信息情景,我们易于获得下述命题:
The high school “Algebra” book P193 has such an example: Find the value of sin~210°+cos~240°+sin10°cos40°. Coincidentally, in recent years, questions similar to this example have (1) find the value of cos ~ 215 ° + cos ~ 275 ° + cos15 ° cos75 °. (’90 national college entrance examination questions) (2) Evaluation: cos~210°+cos~250°-sin~240°sin~280°. (’91 national high school league title) (3) Find the value of sin~220°+sin~280°+2~(1/3)sin~220°cos80°. (’92 national college entrance examination questions) (4) Find the value of cos~210°+sin~240°-cos10°sin40°. (’93 Hunan High School Examination Questions) (5) Find the value of sin~220°+cos~250°+sin20°cos50°. (’95 National College Entrance Examination Questions) From the information scenarios displayed on the examples and exam questions, we can easily obtain the following propositions: