tan15°-tan75°的值为

题目

tan15°-tan75°的值为

答案

tan15°-tan75°
=tan15°-cot15°
=(sin15°/cos15°)-(cos15°/sin15°)
=(sin^215°-cos^215°)/(sin15°*cos15°)
=-cos30°/[(1/2)*sin30°]
=-(1/2)*(√3/2)/(1/2)
=-√3/2