可直接使用正切三倍角公式 tan3θ=tanθtan(60-θ)tan(60+θ). ∴cot15cot25cot35cot85 =tan75(tan65tan55tan5) =tan(90-15)[tan5tan(60-5)tan(60+5)] =cot15tan(3×5) =cot15tan15 =1.
答案是1
cot15°cot25°cot35°cot85° =tan75°tan65°tan55°tan5° =tan75°tan5°(√3+tan5°)/(1-√3tan5°)×(√3-tan5°)/(1+√3tan5°) =tan75°tan5°(3-tan²5°)/(1-3tan²5°) =tan75°tan5°(3cos²5°-sin²5°)/(cos²5°-3sin²5°) =tan75°(2sin5°cos10°+sin5°)/(2cos5°cos10°-cos5°) =tan75°(sin15°-sin5°+sin5°)/(cos15°+cos5°-cos5°) =tan75°tan15° =tan75°cot75° =1 。
答：cot15cot25cot35cot85 =(cos15cos25cos35cos85)/(sin15sin25sin35sin85) 分子=co15(cos2...详情>>
答：详情>>
