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三角函数与几何密不可分,下面给出的几个三角函数求值问题源自于历年各地的高考或竞赛试题,这些试题一般利用高中三角函数知识求解,但通过巧妙构造几何图形仅用初中数学知识就可以解答,在某些时候甚至比利用高中三角函数知识的解答更为简捷.例1求tan67°30’-tan22°30’的值分析:如图1,作Rt△ABC,使∠A=22°30’,BC=1.再作∠ABD=22°30’,则∠BDC=∠A+∠ABD=45°,在等腰直
Triangular function and geometry are inseparable, several trigonometric function evaluation given below originated from around the years college entrance examination or competition test questions, these questions are generally solved using high school trigonometric function knowledge, but by clever construction of geometry using only junior high school mathematics knowledge Can be answered, and in some cases even more simpler than the solution to the knowledge of trigonometry in higher school Example 1 To find the value of tan67 ° 30’-tan22 ° 30 ’: For Rt △ ABC, let ∠A = 22 ° 30 ’, BC = 1. Then ∠ABD = 22 ° 30’, then ∠BDC = ∠A + ∠ABD = 45 °, in the isosceles