还是那道题目,(√3+tan〖15°〗)/(1-√3tan〖15°〗)我没有学过正,余切的半角公式

Answer 1

(√3+tan15°)/(1-√3tan15°)
分子分母同乘以 cos15°
原式=(√3cos15°+sin15°)/(cos15°-√3sin15°)
=(cos30°cos15°+sin30°sin15°)/(cos60°cos15°-sin60°sin15°)
=cos15°/cos75°
=sin75°/cos75°
而 sin75°=sin(45°+30°)
=sin45°cos30°+cos45°sin30°
=√6/4+√2/4
=(√6+√2)/4
cos75°=cos(45°+30°)
=cos45°cos30°-sin45°sin30°
=(√6-√2)/4
所以原式=(√6+√2)/(√6-√2)
=2+√3.