深化拓展：求cot10°-4cos10°的值．

Question

深化拓展：求cot10°-4cos10°的值．

Answer 1

提示：cot10°-4cos10°
=(cos10°)/(sin10°)-4cos10°
=(cos10°−2sin20°)/(sin10°)
=(cos(30°−20°)−2sin20°)/(sin10°)
=((√(3))/(2)cos20°+(1)/(2)sin20°−2sin20°)/(sin10°)
=((√(3))/(2)cos20°−(3)/(2)sin20°)/(sin10°)
=(√(3)sin(30°−20°))/(sin10°)
=√(3)
故答案：√(3)