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在三角函数的和差化积与积化和差的教学中，大多数教师可能注意到这么一道计算题：求ｔｇπ７ｔｇ２π７ｔｇ３π７的值或证明：ｔｇπ７ｔｇ２π７ｔｇ３π７＝７．近日在教学中碰到一题：求证：ｔｇπ５·ｔｇ２π５＝５；结合ｔｇπ３＝３，使我大胆猜想：对ｎ∈Ｎ，有...
In the teaching of trigonometric function sum and difference product and product and difference, most teachers may notice such a calculation problem: find the value of tgπ7tg2π7tg3π7 or prove: tgπ7tg2π7tg3π7=7. Recently encountered a problem in teaching: verification: tgπ5 · tg2π5 = 5; combined tgπ3 = 3, so I boldly guess: for n∈N, there is ...